Answer:
r = 0
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "0.3" was replaced by "(3/10)".
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
r-(5*(c*a-(3/10))*f*o*r*f*o*r*m*u*l*a*c)=0
Step by step solution :
Step 1 :
3
Simplify ——
10
Equation at the end of step 1 :
3
r-((((((((((((5•(ca-——))•f)•o)•r)•f)•o)•r)•m)•u)•l)•a)•c) = 0
10
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 10 as the denominator :
ca ca • 10
ca = —— = ———————
1 10
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
ca • 10 - (3) 10ca - 3
————————————— = ————————
10 10
Equation at the end of step 2 :
(10ca-3)
r-((((((((((((5•————————)•f)•o)•r)•f)•o)•r)•m)•u)•l)•a)•c) = 0
10
Step 3 :
Equation at the end of step 3 :
(10ca-3)
r-(((((((((((————————•f)•o)•r)•f)•o)•r)•m)•u)•l)•a)•c) = 0
2
Step 4 :
Equation at the end of step 4 :
f•(10ca-3)
r-((((((((((——————————•o)•r)•f)•o)•r)•m)•u)•l)•a)•c) = 0
2
Step 5 :
Equation at the end of step 5 :
fo•(10ca-3)
r-(((((((((———————————•r)•f)•o)•r)•m)•u)•l)•a)•c) = 0
2
Step 6 :
Equation at the end of step 6 :
rfo•(10ca-3)
r-((((((((————————————•f)•o)•r)•m)•u)•l)•a)•c) = 0
2
Step 7 :
Multiplying exponential expressions :
7.1 f1 multiplied by f1 = f(1 + 1) = f2
Equation at the end of step 7 :
rf2o•(10ca-3)
r-(((((((—————————————•o)•r)•m)•u)•l)•a)•c) = 0
2
Step 8 :
Multiplying exponential expressions :
8.1 o1 multiplied by o1 = o(1 + 1) = o2
Equation at the end of step 8 :
rf2o2•(10ca-3)
r-((((((——————————————•r)•m)•u)•l)•a)•c) = 0
2
Step 9 :
Multiplying exponential expressions :
9.1 r1 multiplied by r1 = r(1 + 1) = r2
Equation at the end of step 9 :
r2f2o2•(10ca-3)
r-(((((———————————————•m)•u)•l)•a)•c) = 0
2
Step 10 :
Equation at the end of step 10 :
r2f2o2m•(10ca-3)
r-((((————————————————•u)•l)•a)•c) = 0
2
Step 11 :
Equation at the end of step 11 :
r2f2o2mu • (10ca - 3)
r - (((————————————————————— • l) • a) • c) = 0
2
Step 12 :
Equation at the end of step 12 :
r2f2o2mul • (10ca - 3)
r - ((—————————————————————— • a) • c) = 0
2
Step 13 :
Equation at the end of step 13 :
r2af2o2mul • (10ca - 3)
r - (——————————————————————— • c) = 0
2
Step 14 :
Equation at the end of step 14 :
r2caf2o2mul • (10ca - 3)
r - ———————————————————————— = 0
2
Step 15 :
Rewriting the whole as an Equivalent Fraction :
15.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 2 as the denominator :
r r • 2
r = — = —————
1 2
Adding fractions that have a common denominator :
15.2 Adding up the two equivalent fractions
r • 2 - (r2caf2o2mul • (10ca-3)) -10r2c2a2f2o2mul + 3r2caf2o2mul + 2r
———————————————————————————————— = ————————————————————————————————————
2 2
Step 16 :
Pulling out like terms :
16.1 Pull out like factors :
-10r2c2a2f2o2mul + 3r2caf2o2mul + 2r = -r • (10rc2a2f2o2mul - 3rcaf2o2mul - 2)
Trying to factor a multi variable polynomial :
16.2 Factoring 10rc2a2f2o2mul - 3rcaf2o2mul - 2
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Equation at the end of step 16 :
-r • (10rc2a2f2o2mul - 3rcaf2o2mul - 2)
——————————————————————————————————————— = 0
2
Step 17 :
When a fraction equals zero :
17.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
-r•(10rc2a2f2o2mul-3rcaf2o2mul-2)
————————————————————————————————— • 2 = 0 • 2
2
Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
-r • (10rc2a2f2o2mul-3rcaf2o2mul-2) = 0
Theory - Roots of a product :
17.2 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
17.3 Solve : -r = 0
Multiply both sides of the equation by (-1) : r = 0
Step-by-step explanation:
