3x^2-12x+4=76-6x

Solution for 3x^2-12x+4=76-6x equation:

Simplifying
3x2 + -12x + 4 = 76 + -6x

Reorder the terms:
4 + -12x + 3x2 = 76 + -6x

Solving
4 + -12x + 3x2 = 76 + -6x

Solving for variable 'x'.

Reorder the terms:
4 + -76 + -12x + 6x + 3x2 = 76 + -6x + -76 + 6x

Combine like terms: 4 + -76 = -72
-72 + -12x + 6x + 3x2 = 76 + -6x + -76 + 6x

Combine like terms: -12x + 6x = -6x
-72 + -6x + 3x2 = 76 + -6x + -76 + 6x

Reorder the terms:
-72 + -6x + 3x2 = 76 + -76 + -6x + 6x

Combine like terms: 76 + -76 = 0
-72 + -6x + 3x2 = 0 + -6x + 6x
-72 + -6x + 3x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-72 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -2x + x2) = 0

Factor a trinomial.
3((-4 + -1x)(6 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-4, 6}