40=c(c-3)

Solution for 40=c(c-3) equation:

Simplifying
40 = c(c + -3)

Reorder the terms:
40 = c(-3 + c)
40 = (-3 * c + c * c)
40 = (-3c + c2)

Solving
40 = -3c + c2

Solving for variable 'c'.

Reorder the terms:
40 + 3c + -1c2 = -3c + 3c + c2 + -1c2

Combine like terms: -3c + 3c = 0
40 + 3c + -1c2 = 0 + c2 + -1c2
40 + 3c + -1c2 = c2 + -1c2

Combine like terms: c2 + -1c2 = 0
40 + 3c + -1c2 = 0

Factor a trinomial.
(8 + -1c)(5 + 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 '(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 = {8, -5}