0=x^2+11x-80

Solution for 0=x^2+11x-80 equation:

Simplifying
0 = x2 + 11x + -80

Reorder the terms:
0 = -80 + 11x + x2

Solving
0 = -80 + 11x + x2

Solving for variable 'x'.

Combine like terms: 0 + 80 = 80
80 + -11x + -1x2 = -80 + 11x + x2 + 80 + -11x + -1x2

Reorder the terms:
80 + -11x + -1x2 = -80 + 80 + 11x + -11x + x2 + -1x2

Combine like terms: -80 + 80 = 0
80 + -11x + -1x2 = 0 + 11x + -11x + x2 + -1x2
80 + -11x + -1x2 = 11x + -11x + x2 + -1x2

Combine like terms: 11x + -11x = 0
80 + -11x + -1x2 = 0 + x2 + -1x2
80 + -11x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
80 + -11x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(16 + x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16
Solution
x = {5, -16}