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

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


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

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

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

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

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

Reorder the terms:
-14 + 5x + x2 = -2(-2 + x)
-14 + 5x + x2 = (-2 * -2 + x * -2)
-14 + 5x + x2 = (4 + -2x)

Solving
-14 + 5x + x2 = 4 + -2x

Solving for variable 'x'.

Reorder the terms:
-14 + -4 + 5x + 2x + x2 = 4 + -2x + -4 + 2x

Combine like terms: -14 + -4 = -18
-18 + 5x + 2x + x2 = 4 + -2x + -4 + 2x

Combine like terms: 5x + 2x = 7x
-18 + 7x + x2 = 4 + -2x + -4 + 2x

Reorder the terms:
-18 + 7x + x2 = 4 + -4 + -2x + 2x

Combine like terms: 4 + -4 = 0
-18 + 7x + x2 = 0 + -2x + 2x
-18 + 7x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-18 + 7x + x2 = 0

Factor a trinomial.
(-9 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-9, 2}

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