x^2+6x-6+12=78

Solution for x^2+6x-6+12=78 equation:

Simplifying
x2 + 6x + -6 + 12 = 78

Reorder the terms:
-6 + 12 + 6x + x2 = 78

Combine like terms: -6 + 12 = 6
6 + 6x + x2 = 78

Solving
6 + 6x + x2 = 78

Solving for variable 'x'.

Reorder the terms:
6 + -78 + 6x + x2 = 78 + -78

Combine like terms: 6 + -78 = -72
-72 + 6x + x2 = 78 + -78

Combine like terms: 78 + -78 = 0
-72 + 6x + x2 = 0

Factor a trinomial.
(-12 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
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 = {-12, 6}