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

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


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

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

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

Multiply (8 + 7a) * (8 + 5a)
(8(8 + 5a) + 7a * (8 + 5a)) = 0
((8 * 8 + 5a * 8) + 7a * (8 + 5a)) = 0
((64 + 40a) + 7a * (8 + 5a)) = 0
(64 + 40a + (8 * 7a + 5a * 7a)) = 0
(64 + 40a + (56a + 35a2)) = 0

Combine like terms: 40a + 56a = 96a
(64 + 96a + 35a2) = 0

Solving
64 + 96a + 35a2 = 0

Solving for variable 'a'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(8 + 7a)' equal to zero and attempt to solve:

Simplifying
8 + 7a = 0

Solving
8 + 7a = 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 + 7a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7a = 0 + -8
7a = 0 + -8

Combine like terms: 0 + -8 = -8
7a = -8

Divide each side by '7'.
a = -1.142857143

Simplifying
a = -1.142857143
Solution
a = {-1.6, -1.142857143}

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