(12a+7)(5a-8)=0

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Solution for (12a+7)(5a-8)=0 equation: 


Simplifying
(12a + 7)(5a + -8) = 0

Reorder the terms:
(7 + 12a)(5a + -8) = 0

Reorder the terms:
(7 + 12a)(-8 + 5a) = 0

Multiply (7 + 12a) * (-8 + 5a)
(7(-8 + 5a) + 12a * (-8 + 5a)) = 0
((-8 * 7 + 5a * 7) + 12a * (-8 + 5a)) = 0
((-56 + 35a) + 12a * (-8 + 5a)) = 0
(-56 + 35a + (-8 * 12a + 5a * 12a)) = 0
(-56 + 35a + (-96a + 60a2)) = 0

Combine like terms: 35a + -96a = -61a
(-56 + -61a + 60a2) = 0

Solving
-56 + -61a + 60a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -12a)(8 + -5a) = 0


Subproblem 1
Set the factor '(-7 + -12a)' equal to zero and attempt to solve:

Simplifying
-7 + -12a = 0

Solving
-7 + -12a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -12a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -12a = 0 + 7
-12a = 0 + 7

Combine like terms: 0 + 7 = 7
-12a = 7

Divide each side by '-12'.
a = -0.5833333333

Simplifying
a = -0.5833333333

Subproblem 2
Set the factor '(8 + -5a)' equal to zero and attempt to solve:

Simplifying
8 + -5a = 0

Solving
8 + -5a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5a = 0 + -8
-5a = 0 + -8

Combine like terms: 0 + -8 = -8
-5a = -8

Divide each side by '-5'.
a = 1.6

Simplifying
a = 1.6
Solution
a = {-0.5833333333, 1.6}

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