24=c(c-5)

Solution for 24=c(c-5) equation:

Simplifying
24 = c(c + -5)

Reorder the terms:
24 = c(-5 + c)
24 = (-5 * c + c * c)
24 = (-5c + c2)

Solving
24 = -5c + c2

Solving for variable 'c'.

Reorder the terms:
24 + 5c + -1c2 = -5c + 5c + c2 + -1c2

Combine like terms: -5c + 5c = 0
24 + 5c + -1c2 = 0 + c2 + -1c2
24 + 5c + -1c2 = c2 + -1c2

Combine like terms: c2 + -1c2 = 0
24 + 5c + -1c2 = 0

Factor a trinomial.
(8 + -1c)(3 + c) = 0

Subproblem 1
Set the factor '(8 + -1c)' equal to zero and attempt to solve:

Simplifying
8 + -1c = 0

Solving
8 + -1c = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1c = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1c = 0 + -8
-1c = 0 + -8

Combine like terms: 0 + -8 = -8
-1c = -8

Divide each side by '-1'.
c = 8

Simplifying
c = 8
Subproblem 2
Set the factor '(3 + c)' equal to zero and attempt to solve:

Simplifying
3 + c = 0

Solving
3 + c = 0

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

Add '-3' to each side of the equation.
3 + -3 + c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + c = 0 + -3
c = 0 + -3

Combine like terms: 0 + -3 = -3
c = -3

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