(x-2)(x+4)=-2(x-12)

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Solution for (x-2)(x+4)=-2(x-12) equation: 


Simplifying
(x + -2)(x + 4) = -2(x + -12)

Reorder the terms:
(-2 + x)(x + 4) = -2(x + -12)

Reorder the terms:
(-2 + x)(4 + x) = -2(x + -12)

Multiply (-2 + x) * (4 + x)
(-2(4 + x) + x(4 + x)) = -2(x + -12)
((4 * -2 + x * -2) + x(4 + x)) = -2(x + -12)
((-8 + -2x) + x(4 + x)) = -2(x + -12)
(-8 + -2x + (4 * x + x * x)) = -2(x + -12)
(-8 + -2x + (4x + x2)) = -2(x + -12)

Combine like terms: -2x + 4x = 2x
(-8 + 2x + x2) = -2(x + -12)

Reorder the terms:
-8 + 2x + x2 = -2(-12 + x)
-8 + 2x + x2 = (-12 * -2 + x * -2)
-8 + 2x + x2 = (24 + -2x)

Solving
-8 + 2x + x2 = 24 + -2x

Solving for variable 'x'.

Reorder the terms:
-8 + -24 + 2x + 2x + x2 = 24 + -2x + -24 + 2x

Combine like terms: -8 + -24 = -32
-32 + 2x + 2x + x2 = 24 + -2x + -24 + 2x

Combine like terms: 2x + 2x = 4x
-32 + 4x + x2 = 24 + -2x + -24 + 2x

Reorder the terms:
-32 + 4x + x2 = 24 + -24 + -2x + 2x

Combine like terms: 24 + -24 = 0
-32 + 4x + x2 = 0 + -2x + 2x
-32 + 4x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-32 + 4x + x2 = 0

Factor a trinomial.
(-8 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-8, 4}

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