4x^2-6x+8=6x-3+3x^2

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Solution for 4x^2-6x+8=6x-3+3x^2 equation: 


Simplifying
4x2 + -6x + 8 = 6x + -3 + 3x2

Reorder the terms:
8 + -6x + 4x2 = 6x + -3 + 3x2

Reorder the terms:
8 + -6x + 4x2 = -3 + 6x + 3x2

Solving
8 + -6x + 4x2 = -3 + 6x + 3x2

Solving for variable 'x'.

Reorder the terms:
8 + 3 + -6x + -6x + 4x2 + -3x2 = -3 + 6x + 3x2 + 3 + -6x + -3x2

Combine like terms: 8 + 3 = 11
11 + -6x + -6x + 4x2 + -3x2 = -3 + 6x + 3x2 + 3 + -6x + -3x2

Combine like terms: -6x + -6x = -12x
11 + -12x + 4x2 + -3x2 = -3 + 6x + 3x2 + 3 + -6x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
11 + -12x + 1x2 = -3 + 6x + 3x2 + 3 + -6x + -3x2

Reorder the terms:
11 + -12x + 1x2 = -3 + 3 + 6x + -6x + 3x2 + -3x2

Combine like terms: -3 + 3 = 0
11 + -12x + 1x2 = 0 + 6x + -6x + 3x2 + -3x2
11 + -12x + 1x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
11 + -12x + 1x2 = 0 + 3x2 + -3x2
11 + -12x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
11 + -12x + 1x2 = 0

Factor a trinomial.
(1 + -1x)(11 + -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 '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {1, 11}

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