x^2-3x+4+8x^2-12x+8-6x-6=0

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Solution for x^2-3x+4+8x^2-12x+8-6x-6=0 equation: 


Simplifying
x2 + -3x + 4 + 8x2 + -12x + 8 + -6x + -6 = 0

Reorder the terms:
4 + 8 + -6 + -3x + -12x + -6x + x2 + 8x2 = 0

Combine like terms: 4 + 8 = 12
12 + -6 + -3x + -12x + -6x + x2 + 8x2 = 0

Combine like terms: 12 + -6 = 6
6 + -3x + -12x + -6x + x2 + 8x2 = 0

Combine like terms: -3x + -12x = -15x
6 + -15x + -6x + x2 + 8x2 = 0

Combine like terms: -15x + -6x = -21x
6 + -21x + x2 + 8x2 = 0

Combine like terms: x2 + 8x2 = 9x2
6 + -21x + 9x2 = 0

Solving
6 + -21x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -7x + 3x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

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 = {0.3333333333, 2}

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