x^2-12x-91=-6

Solution for x^2-12x-91=-6 equation:

Simplifying
x2 + -12x + -91 = -6

Reorder the terms:
-91 + -12x + x2 = -6

Solving
-91 + -12x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
-91 + 6 + -12x + x2 = -6 + 6

Combine like terms: -91 + 6 = -85
-85 + -12x + x2 = -6 + 6

Combine like terms: -6 + 6 = 0
-85 + -12x + x2 = 0

Factor a trinomial.
(-5 + -1x)(17 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {-5, 17}