x^2-1=6x+6

Solution for x^2-1=6x+6 equation:

Simplifying
x2 + -1 = 6x + 6

Reorder the terms:
-1 + x2 = 6x + 6

Reorder the terms:
-1 + x2 = 6 + 6x

Solving
-1 + x2 = 6 + 6x

Solving for variable 'x'.

Reorder the terms:
-1 + -6 + -6x + x2 = 6 + 6x + -6 + -6x

Combine like terms: -1 + -6 = -7
-7 + -6x + x2 = 6 + 6x + -6 + -6x

Reorder the terms:
-7 + -6x + x2 = 6 + -6 + 6x + -6x

Combine like terms: 6 + -6 = 0
-7 + -6x + x2 = 0 + 6x + -6x
-7 + -6x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-7 + -6x + x2 = 0

Factor a trinomial.
(-1 + -1x)(7 + -1x) = 0

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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1, 7}