c^2=5c-6

Solution for c^2=5c-6 equation:

Simplifying
c2 = 5c + -6

Reorder the terms:
c2 = -6 + 5c

Solving
c2 = -6 + 5c

Solving for variable 'c'.

Reorder the terms:
6 + -5c + c2 = -6 + 5c + 6 + -5c

Reorder the terms:
6 + -5c + c2 = -6 + 6 + 5c + -5c

Combine like terms: -6 + 6 = 0
6 + -5c + c2 = 0 + 5c + -5c
6 + -5c + c2 = 5c + -5c

Combine like terms: 5c + -5c = 0
6 + -5c + c2 = 0

Factor a trinomial.
(2 + -1c)(3 + -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 '(3 + -1c)' equal to zero and attempt to solve:

Simplifying
3 + -1c = 0

Solving
3 + -1c = 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 + -1c = 0 + -3

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

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

Divide each side by '-1'.
c = 3

Simplifying
c = 3
Solution
c = {2, 3}