(x-7)(x+8)=-(x+8)

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Solution for (x-7)(x+8)=-(x+8) equation: 


Simplifying
(x + -7)(x + 8) = -1(x + 8)

Reorder the terms:
(-7 + x)(x + 8) = -1(x + 8)

Reorder the terms:
(-7 + x)(8 + x) = -1(x + 8)

Multiply (-7 + x) * (8 + x)
(-7(8 + x) + x(8 + x)) = -1(x + 8)
((8 * -7 + x * -7) + x(8 + x)) = -1(x + 8)
((-56 + -7x) + x(8 + x)) = -1(x + 8)
(-56 + -7x + (8 * x + x * x)) = -1(x + 8)
(-56 + -7x + (8x + x2)) = -1(x + 8)

Combine like terms: -7x + 8x = 1x
(-56 + 1x + x2) = -1(x + 8)

Reorder the terms:
-56 + 1x + x2 = -1(8 + x)
-56 + 1x + x2 = (8 * -1 + x * -1)
-56 + 1x + x2 = (-8 + -1x)

Solving
-56 + 1x + x2 = -8 + -1x

Solving for variable 'x'.

Reorder the terms:
-56 + 8 + 1x + x + x2 = -8 + -1x + 8 + x

Combine like terms: -56 + 8 = -48
-48 + 1x + x + x2 = -8 + -1x + 8 + x

Combine like terms: 1x + x = 2x
-48 + 2x + x2 = -8 + -1x + 8 + x

Reorder the terms:
-48 + 2x + x2 = -8 + 8 + -1x + x

Combine like terms: -8 + 8 = 0
-48 + 2x + x2 = 0 + -1x + x
-48 + 2x + x2 = -1x + x

Combine like terms: -1x + x = 0
-48 + 2x + x2 = 0

Factor a trinomial.
(-8 + -1x)(6 + -1x) = 0


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

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

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

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

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

Simplifying
x = -8

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-8, 6}

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