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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}
Answer and Explanation:
The journal entries are shown below:
1. On Sep 30
Cash $15750
To Sales $15,000
To Sales taxes payable ($15000 ×5%) $750
(Being the cash receipts is recorded)
For recording this we debited the cash as it increased the assets and credited the sales and sales tax payable as it increased the revenue and liabilities
2 On Sep 30
Cost of goods sold $12,000
To Merchandise inventory $12,000
(Being the cost of goods sold is recorded)
For recording this we debited the cost of goods sold as it increased the expenses and credited the merchandise inventory as it reduced the assets
3 On Oct 15
Sales taxes payable $750
To Cash $750
(Being cash paid is recorded)
For recording this we debited the sales tax payable as it reduced the liabilities and credited the cash as it decreased the assets
