2x=6x-12+8x^2

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Solution for 2x=6x-12+8x^2 equation: 


Simplifying
2x = 6x + -12 + 8x2

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

Solving
2x = -12 + 6x + 8x2

Solving for variable 'x'.

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

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

Reorder the terms:
12 + -4x + -8x2 = -12 + 12 + 6x + -6x + 8x2 + -8x2

Combine like terms: -12 + 12 = 0
12 + -4x + -8x2 = 0 + 6x + -6x + 8x2 + -8x2
12 + -4x + -8x2 = 6x + -6x + 8x2 + -8x2

Combine like terms: 6x + -6x = 0
12 + -4x + -8x2 = 0 + 8x2 + -8x2
12 + -4x + -8x2 = 8x2 + -8x2

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

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -1x + -2x2) = 0

Factor a trinomial.
4((1 + -1x)(3 + 2x)) = 0

Ignore the factor 4.

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 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {1, -1.5}

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