x^2+6x-6=1

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

Simplifying
x2 + 6x + -6 = 1

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

Solving
-6 + 6x + x2 = 1

Solving for variable 'x'.

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

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

Combine like terms: 1 + -1 = 0
-7 + 6x + x2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-7, 1}