2x^2-2x-8=4x+12

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


Simplifying
2x2 + -2x + -8 = 4x + 12

Reorder the terms:
-8 + -2x + 2x2 = 4x + 12

Reorder the terms:
-8 + -2x + 2x2 = 12 + 4x

Solving
-8 + -2x + 2x2 = 12 + 4x

Solving for variable 'x'.

Reorder the terms:
-8 + -12 + -2x + -4x + 2x2 = 12 + 4x + -12 + -4x

Combine like terms: -8 + -12 = -20
-20 + -2x + -4x + 2x2 = 12 + 4x + -12 + -4x

Combine like terms: -2x + -4x = -6x
-20 + -6x + 2x2 = 12 + 4x + -12 + -4x

Reorder the terms:
-20 + -6x + 2x2 = 12 + -12 + 4x + -4x

Combine like terms: 12 + -12 = 0
-20 + -6x + 2x2 = 0 + 4x + -4x
-20 + -6x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-20 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -3x + x2) = 0

Factor a trinomial.
2((-2 + -1x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-2, 5}

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