(x-4)(x+8)=2(x-12)

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Solution for (x-4)(x+8)=2(x-12) equation: 


Simplifying
(x + -4)(x + 8) = 2(x + -12)

Reorder the terms:
(-4 + x)(x + 8) = 2(x + -12)

Reorder the terms:
(-4 + x)(8 + x) = 2(x + -12)

Multiply (-4 + x) * (8 + x)
(-4(8 + x) + x(8 + x)) = 2(x + -12)
((8 * -4 + x * -4) + x(8 + x)) = 2(x + -12)
((-32 + -4x) + x(8 + x)) = 2(x + -12)
(-32 + -4x + (8 * x + x * x)) = 2(x + -12)
(-32 + -4x + (8x + x2)) = 2(x + -12)

Combine like terms: -4x + 8x = 4x
(-32 + 4x + x2) = 2(x + -12)

Reorder the terms:
-32 + 4x + x2 = 2(-12 + x)
-32 + 4x + x2 = (-12 * 2 + x * 2)
-32 + 4x + x2 = (-24 + 2x)

Solving
-32 + 4x + x2 = -24 + 2x

Solving for variable 'x'.

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

Combine like terms: -32 + 24 = -8
-8 + 4x + -2x + x2 = -24 + 2x + 24 + -2x

Combine like terms: 4x + -2x = 2x
-8 + 2x + x2 = -24 + 2x + 24 + -2x

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

Combine like terms: -24 + 24 = 0
-8 + 2x + x2 = 0 + 2x + -2x
-8 + 2x + x2 = 2x + -2x

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

Factor a trinomial.
(-4 + -1x)(2 + -1x) = 0


Subproblem 1
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

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 = {-4, 2}

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