3x^2-12x+6=2x^2-8x+3

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Solution for 3x^2-12x+6=2x^2-8x+3 equation: 


Simplifying
3x2 + -12x + 6 = 2x2 + -8x + 3

Reorder the terms:
6 + -12x + 3x2 = 2x2 + -8x + 3

Reorder the terms:
6 + -12x + 3x2 = 3 + -8x + 2x2

Solving
6 + -12x + 3x2 = 3 + -8x + 2x2

Solving for variable 'x'.

Reorder the terms:
6 + -3 + -12x + 8x + 3x2 + -2x2 = 3 + -8x + 2x2 + -3 + 8x + -2x2

Combine like terms: 6 + -3 = 3
3 + -12x + 8x + 3x2 + -2x2 = 3 + -8x + 2x2 + -3 + 8x + -2x2

Combine like terms: -12x + 8x = -4x
3 + -4x + 3x2 + -2x2 = 3 + -8x + 2x2 + -3 + 8x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
3 + -4x + 1x2 = 3 + -8x + 2x2 + -3 + 8x + -2x2

Reorder the terms:
3 + -4x + 1x2 = 3 + -3 + -8x + 8x + 2x2 + -2x2

Combine like terms: 3 + -3 = 0
3 + -4x + 1x2 = 0 + -8x + 8x + 2x2 + -2x2
3 + -4x + 1x2 = -8x + 8x + 2x2 + -2x2

Combine like terms: -8x + 8x = 0
3 + -4x + 1x2 = 0 + 2x2 + -2x2
3 + -4x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3 + -4x + 1x2 = 0

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


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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