Question

(-2a+5)(3a+4) 5)(3a + 4)" alt="( - 2a + 5)(3a + 4)" align="absmiddle" class="latex-formula">
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Answer 1

Simplifying
(2a + 5)(3a + -4) = 0

Reorder the terms:
(5 + 2a)(3a + -4) = 0

Reorder the terms:
(5 + 2a)(-4 + 3a) = 0

Multiply (5 + 2a) * (-4 + 3a)
(5(-4 + 3a) + 2a * (-4 + 3a)) = 0
((-4 * 5 + 3a * 5) + 2a * (-4 + 3a)) = 0
((-20 + 15a) + 2a * (-4 + 3a)) = 0
(-20 + 15a + (-4 * 2a + 3a * 2a)) = 0
(-20 + 15a + (-8a + 6a2)) = 0

Combine like terms: 15a + -8a = 7a
(-20 + 7a + 6a2) = 0

Solving
-20 + 7a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -2a)(4 + -3a) = 0

Subproblem 1
Set the factor '(-5 + -2a)' equal to zero and attempt to solve:

Simplifying
-5 + -2a = 0

Solving
-5 + -2a = 0

Move all terms containing a to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -2a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2a = 0 + 5
-2a = 0 + 5

Combine like terms: 0 + 5 = 5
-2a = 5

Divide each side by '-2'.
a = -2.5

Simplifying
a = -2.5
Subproblem 2
Set the factor '(4 + -3a)' equal to zero and attempt to solve:

Simplifying
4 + -3a = 0

Solving
4 + -3a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -3a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3a = 0 + -4
-3a = 0 + -4

Combine like terms: 0 + -4 = -4
-3a = -4

Divide each side by '-3'.
a = 1.333333333

Simplifying
a = 1.333333333
Solution
a = {-2.5, 1.333333333}