50=c(c-5)

Solution for 50=c(c-5) equation:

Simplifying
50 = c(c + -5)

Reorder the terms:
50 = c(-5 + c)
50 = (-5 * c + c * c)
50 = (-5c + c2)

Solving
50 = -5c + c2

Solving for variable 'c'.

Reorder the terms:
50 + 5c + -1c2 = -5c + 5c + c2 + -1c2

Combine like terms: -5c + 5c = 0
50 + 5c + -1c2 = 0 + c2 + -1c2
50 + 5c + -1c2 = c2 + -1c2

Combine like terms: c2 + -1c2 = 0
50 + 5c + -1c2 = 0

Factor a trinomial.
(10 + -1c)(5 + c) = 0

Subproblem 1
Set the factor '(10 + -1c)' equal to zero and attempt to solve:

Simplifying
10 + -1c = 0

Solving
10 + -1c = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1c = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1c = 0 + -10
-1c = 0 + -10

Combine like terms: 0 + -10 = -10
-1c = -10

Divide each side by '-1'.
c = 10

Simplifying
c = 10
Subproblem 2
Set the factor '(5 + c)' equal to zero and attempt to solve:

Simplifying
5 + c = 0

Solving
5 + c = 0

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

Add '-5' to each side of the equation.
5 + -5 + c = 0 + -5

Combine like terms: 5 + -5 = 0
0 + c = 0 + -5
c = 0 + -5

Combine like terms: 0 + -5 = -5
c = -5

Simplifying
c = -5
Solution
c = {10, -5}