2x=4x-8+6x^2

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Solution for 2x=4x-8+6x^2 equation: 


Simplifying
2x = 4x + -8 + 6x2

Reorder the terms:
2x = -8 + 4x + 6x2

Solving
2x = -8 + 4x + 6x2

Solving for variable 'x'.

Reorder the terms:
8 + 2x + -4x + -6x2 = -8 + 4x + 6x2 + 8 + -4x + -6x2

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

Reorder the terms:
8 + -2x + -6x2 = -8 + 8 + 4x + -4x + 6x2 + -6x2

Combine like terms: -8 + 8 = 0
8 + -2x + -6x2 = 0 + 4x + -4x + 6x2 + -6x2
8 + -2x + -6x2 = 4x + -4x + 6x2 + -6x2

Combine like terms: 4x + -4x = 0
8 + -2x + -6x2 = 0 + 6x2 + -6x2
8 + -2x + -6x2 = 6x2 + -6x2

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

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

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

Ignore the factor 2.

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 '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 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 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {1, -1.333333333}

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