-x^2-5x=-24

Solution for -x^2-5x=-24 equation:

Simplifying
-1x2 + -5x = -24

Reorder the terms:
-5x + -1x2 = -24

Solving
-5x + -1x2 = -24

Solving for variable 'x'.

Reorder the terms:
24 + -5x + -1x2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + -5x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(8 + 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 '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {3, -8}