0=x^2-8x-33

Solution for 0=x^2-8x-33 equation:

Simplifying
0 = x2 + -8x + -33

Reorder the terms:
0 = -33 + -8x + x2

Solving
0 = -33 + -8x + x2

Solving for variable 'x'.

Combine like terms: 0 + 33 = 33
33 + 8x + -1x2 = -33 + -8x + x2 + 33 + 8x + -1x2

Reorder the terms:
33 + 8x + -1x2 = -33 + 33 + -8x + 8x + x2 + -1x2

Combine like terms: -33 + 33 = 0
33 + 8x + -1x2 = 0 + -8x + 8x + x2 + -1x2
33 + 8x + -1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
33 + 8x + -1x2 = 0 + x2 + -1x2
33 + 8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
33 + 8x + -1x2 = 0

Factor a trinomial.
(11 + -1x)(3 + x) = 0

Subproblem 1
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {11, -3}