12(x^2-3x)+8=56

Solution for 12(x^2-3x)+8=56 equation:

Simplifying
12(x2 + -3x) + 8 = 56

Reorder the terms:
12(-3x + x2) + 8 = 56
(-3x * 12 + x2 * 12) + 8 = 56
(-36x + 12x2) + 8 = 56

Reorder the terms:
8 + -36x + 12x2 = 56

Solving
8 + -36x + 12x2 = 56

Solving for variable 'x'.

Reorder the terms:
8 + -56 + -36x + 12x2 = 56 + -56

Combine like terms: 8 + -56 = -48
-48 + -36x + 12x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-48 + -36x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-4 + -3x + x2) = 0

Factor a trinomial.
12((-1 + -1x)(4 + -1x)) = 0

Ignore the factor 12.
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 '(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
Solution
x = {-1, 4}