4x^2-4x-4=14+8x-2x^2

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Solution for 4x^2-4x-4=14+8x-2x^2 equation: 


Simplifying
4x2 + -4x + -4 = 14 + 8x + -2x2

Reorder the terms:
-4 + -4x + 4x2 = 14 + 8x + -2x2

Solving
-4 + -4x + 4x2 = 14 + 8x + -2x2

Solving for variable 'x'.

Reorder the terms:
-4 + -14 + -4x + -8x + 4x2 + 2x2 = 14 + 8x + -2x2 + -14 + -8x + 2x2

Combine like terms: -4 + -14 = -18
-18 + -4x + -8x + 4x2 + 2x2 = 14 + 8x + -2x2 + -14 + -8x + 2x2

Combine like terms: -4x + -8x = -12x
-18 + -12x + 4x2 + 2x2 = 14 + 8x + -2x2 + -14 + -8x + 2x2

Combine like terms: 4x2 + 2x2 = 6x2
-18 + -12x + 6x2 = 14 + 8x + -2x2 + -14 + -8x + 2x2

Reorder the terms:
-18 + -12x + 6x2 = 14 + -14 + 8x + -8x + -2x2 + 2x2

Combine like terms: 14 + -14 = 0
-18 + -12x + 6x2 = 0 + 8x + -8x + -2x2 + 2x2
-18 + -12x + 6x2 = 8x + -8x + -2x2 + 2x2

Combine like terms: 8x + -8x = 0
-18 + -12x + 6x2 = 0 + -2x2 + 2x2
-18 + -12x + 6x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-18 + -12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + -2x + x2) = 0

Factor a trinomial.
6((-1 + -1x)(3 + -1x)) = 0

Ignore the factor 6.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1, 3}

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