(x-7)(x+2)=-8(x-5)

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Solution for (x-7)(x+2)=-8(x-5) equation: 


Simplifying
(x + -7)(x + 2) = -8(x + -5)

Reorder the terms:
(-7 + x)(x + 2) = -8(x + -5)

Reorder the terms:
(-7 + x)(2 + x) = -8(x + -5)

Multiply (-7 + x) * (2 + x)
(-7(2 + x) + x(2 + x)) = -8(x + -5)
((2 * -7 + x * -7) + x(2 + x)) = -8(x + -5)
((-14 + -7x) + x(2 + x)) = -8(x + -5)
(-14 + -7x + (2 * x + x * x)) = -8(x + -5)
(-14 + -7x + (2x + x2)) = -8(x + -5)

Combine like terms: -7x + 2x = -5x
(-14 + -5x + x2) = -8(x + -5)

Reorder the terms:
-14 + -5x + x2 = -8(-5 + x)
-14 + -5x + x2 = (-5 * -8 + x * -8)
-14 + -5x + x2 = (40 + -8x)

Solving
-14 + -5x + x2 = 40 + -8x

Solving for variable 'x'.

Reorder the terms:
-14 + -40 + -5x + 8x + x2 = 40 + -8x + -40 + 8x

Combine like terms: -14 + -40 = -54
-54 + -5x + 8x + x2 = 40 + -8x + -40 + 8x

Combine like terms: -5x + 8x = 3x
-54 + 3x + x2 = 40 + -8x + -40 + 8x

Reorder the terms:
-54 + 3x + x2 = 40 + -40 + -8x + 8x

Combine like terms: 40 + -40 = 0
-54 + 3x + x2 = 0 + -8x + 8x
-54 + 3x + x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-54 + 3x + x2 = 0

Factor a trinomial.
(-9 + -1x)(6 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

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 = {-9, 6}

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