0=x^2+24x-81

Solution for 0=x^2+24x-81 equation:

Simplifying
0 = x2 + 24x + -81

Reorder the terms:
0 = -81 + 24x + x2

Solving
0 = -81 + 24x + x2

Solving for variable 'x'.

Combine like terms: 0 + 81 = 81
81 + -24x + -1x2 = -81 + 24x + x2 + 81 + -24x + -1x2

Reorder the terms:
81 + -24x + -1x2 = -81 + 81 + 24x + -24x + x2 + -1x2

Combine like terms: -81 + 81 = 0
81 + -24x + -1x2 = 0 + 24x + -24x + x2 + -1x2
81 + -24x + -1x2 = 24x + -24x + x2 + -1x2

Combine like terms: 24x + -24x = 0
81 + -24x + -1x2 = 0 + x2 + -1x2
81 + -24x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
81 + -24x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(27 + x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(27 + x)' equal to zero and attempt to solve:

Simplifying
27 + x = 0

Solving
27 + x = 0

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

Add '-27' to each side of the equation.
27 + -27 + x = 0 + -27

Combine like terms: 27 + -27 = 0
0 + x = 0 + -27
x = 0 + -27

Combine like terms: 0 + -27 = -27
x = -27

Simplifying
x = -27
Solution
x = {3, -27}