x^2-12x-5=8

Solution for x^2-12x-5=8 equation:

Simplifying
x2 + -12x + -5 = 8

Reorder the terms:
-5 + -12x + x2 = 8

Solving
-5 + -12x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
-5 + -8 + -12x + x2 = 8 + -8

Combine like terms: -5 + -8 = -13
-13 + -12x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-13 + -12x + x2 = 0

Factor a trinomial.
(-1 + -1x)(13 + -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 '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-1, 13}