c(c-3)=10

Solution for c(c-3)=10 equation:

Simplifying
c(c + -3) = 10

Reorder the terms:
c(-3 + c) = 10
(-3 * c + c * c) = 10
(-3c + c2) = 10

Solving
-3c + c2 = 10

Solving for variable 'c'.

Reorder the terms:
-10 + -3c + c2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -3c + c2 = 0

Factor a trinomial.
(-2 + -1c)(5 + -1c) = 0

Subproblem 1
Set the factor '(-2 + -1c)' equal to zero and attempt to solve:

Simplifying
-2 + -1c = 0

Solving
-2 + -1c = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1c = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1c = 0 + 2
-1c = 0 + 2

Combine like terms: 0 + 2 = 2
-1c = 2

Divide each side by '-1'.
c = -2

Simplifying
c = -2
Subproblem 2
Set the factor '(5 + -1c)' equal to zero and attempt to solve:

Simplifying
5 + -1c = 0

Solving
5 + -1c = 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 + -1c = 0 + -5

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

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

Divide each side by '-1'.
c = 5

Simplifying
c = 5
Solution
c = {-2, 5}