3x^2-4x=8-2x

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Solution for 3x^2-4x=8-2x equation: 


Simplifying
3x2 + -4x = 8 + -2x

Reorder the terms:
-4x + 3x2 = 8 + -2x

Solving
-4x + 3x2 = 8 + -2x

Solving for variable 'x'.

Reorder the terms:
-8 + -4x + 2x + 3x2 = 8 + -2x + -8 + 2x

Combine like terms: -4x + 2x = -2x
-8 + -2x + 3x2 = 8 + -2x + -8 + 2x

Reorder the terms:
-8 + -2x + 3x2 = 8 + -8 + -2x + 2x

Combine like terms: 8 + -8 = 0
-8 + -2x + 3x2 = 0 + -2x + 2x
-8 + -2x + 3x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-8 + -2x + 3x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-1.333333333, 2}

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