0=x^2-5x-6

Solution for 0=x^2-5x-6 equation:

Simplifying
0 = x2 + -5x + -6

Reorder the terms:
0 = -6 + -5x + x2

Solving
0 = -6 + -5x + x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + 5x + -1x2 = -6 + -5x + x2 + 6 + 5x + -1x2

Reorder the terms:
6 + 5x + -1x2 = -6 + 6 + -5x + 5x + x2 + -1x2

Combine like terms: -6 + 6 = 0
6 + 5x + -1x2 = 0 + -5x + 5x + x2 + -1x2
6 + 5x + -1x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
6 + 5x + -1x2 = 0 + x2 + -1x2
6 + 5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 5x + -1x2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {6, -1}