6x^2-48x-42=12

Solution for 6x^2-48x-42=12 equation:

Simplifying
6x2 + -48x + -42 = 12

Reorder the terms:
-42 + -48x + 6x2 = 12

Solving
-42 + -48x + 6x2 = 12

Solving for variable 'x'.

Reorder the terms:
-42 + -12 + -48x + 6x2 = 12 + -12

Combine like terms: -42 + -12 = -54
-54 + -48x + 6x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-54 + -48x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-9 + -8x + x2) = 0

Factor a trinomial.
6((-1 + -1x)(9 + -1x)) = 0

Ignore the factor 6.
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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-1, 9}