6c^2-12c=18

Solution for 6c^2-12c=18 equation:

Simplifying
6c2 + -12c = 18

Reorder the terms:
-12c + 6c2 = 18

Solving
-12c + 6c2 = 18

Solving for variable 'c'.

Reorder the terms:
-18 + -12c + 6c2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + -12c + 6c2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + -2c + c2) = 0

Factor a trinomial.
6((-1 + -1c)(3 + -1c)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -1c)' equal to zero and attempt to solve:

Simplifying
-1 + -1c = 0

Solving
-1 + -1c = 0

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

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

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

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

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

Simplifying
c = -1
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 = {-1, 3}