x^2-4x+4=2x^2+4x+16

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Solution for x^2-4x+4=2x^2+4x+16 equation: 


Simplifying
x2 + -4x + 4 = 2x2 + 4x + 16

Reorder the terms:
4 + -4x + x2 = 2x2 + 4x + 16

Reorder the terms:
4 + -4x + x2 = 16 + 4x + 2x2

Solving
4 + -4x + x2 = 16 + 4x + 2x2

Solving for variable 'x'.

Reorder the terms:
4 + -16 + -4x + -4x + x2 + -2x2 = 16 + 4x + 2x2 + -16 + -4x + -2x2

Combine like terms: 4 + -16 = -12
-12 + -4x + -4x + x2 + -2x2 = 16 + 4x + 2x2 + -16 + -4x + -2x2

Combine like terms: -4x + -4x = -8x
-12 + -8x + x2 + -2x2 = 16 + 4x + 2x2 + -16 + -4x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-12 + -8x + -1x2 = 16 + 4x + 2x2 + -16 + -4x + -2x2

Reorder the terms:
-12 + -8x + -1x2 = 16 + -16 + 4x + -4x + 2x2 + -2x2

Combine like terms: 16 + -16 = 0
-12 + -8x + -1x2 = 0 + 4x + -4x + 2x2 + -2x2
-12 + -8x + -1x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
-12 + -8x + -1x2 = 0 + 2x2 + -2x2
-12 + -8x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-12 + -8x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 8x + x2) = 0

Factor a trinomial.
-1((6 + x)(2 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {-6, -2}

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