-24=x^2+10x

Solution for -24=x^2+10x equation:

Simplifying
-24 = x2 + 10x

Reorder the terms:
-24 = 10x + x2

Solving
-24 = 10x + x2

Solving for variable 'x'.

Reorder the terms:
-24 + -10x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-24 + -10x + -1x2 = 0 + x2 + -1x2
-24 + -10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-24 + -10x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(24 + 10x + x2) = 0

Factor a trinomial.
-1((6 + x)(4 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-6, -4}