(a-8)(a+7)=-2a

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Solution for (a-8)(a+7)=-2a equation: 


Simplifying
(a + -8)(a + 7) = -2a

Reorder the terms:
(-8 + a)(a + 7) = -2a

Reorder the terms:
(-8 + a)(7 + a) = -2a

Multiply (-8 + a) * (7 + a)
(-8(7 + a) + a(7 + a)) = -2a
((7 * -8 + a * -8) + a(7 + a)) = -2a
((-56 + -8a) + a(7 + a)) = -2a
(-56 + -8a + (7 * a + a * a)) = -2a
(-56 + -8a + (7a + a2)) = -2a

Combine like terms: -8a + 7a = -1a
(-56 + -1a + a2) = -2a

Solving
-56 + -1a + a2 = -2a

Solving for variable 'a'.

Reorder the terms:
-56 + -1a + 2a + a2 = -2a + 2a

Combine like terms: -1a + 2a = 1a
-56 + 1a + a2 = -2a + 2a

Combine like terms: -2a + 2a = 0
-56 + 1a + a2 = 0

Factor a trinomial.
(-8 + -1a)(7 + -1a) = 0


Subproblem 1
Set the factor '(-8 + -1a)' equal to zero and attempt to solve:

Simplifying
-8 + -1a = 0

Solving
-8 + -1a = 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 + -1a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1a = 0 + 8
-1a = 0 + 8

Combine like terms: 0 + 8 = 8
-1a = 8

Divide each side by '-1'.
a = -8

Simplifying
a = -8

Subproblem 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 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 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {-8, 7}

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