c^2+10c=-24

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

Simplifying
c2 + 10c = -24

Reorder the terms:
10c + c2 = -24

Solving
10c + c2 = -24

Solving for variable 'c'.

Reorder the terms:
24 + 10c + c2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + 10c + c2 = 0

Factor a trinomial.
(6 + c)(4 + c) = 0

Subproblem 1
Set the factor '(6 + c)' equal to zero and attempt to solve:

Simplifying
6 + c = 0

Solving
6 + c = 0

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

Add '-6' to each side of the equation.
6 + -6 + c = 0 + -6

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

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

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

Simplifying
4 + c = 0

Solving
4 + c = 0

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

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

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

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

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