6c^2+6c-252=0

Solution for 6c^2+6c-252=0 equation:

Simplifying
6c2 + 6c + -252 = 0

Reorder the terms:
-252 + 6c + 6c2 = 0

Solving
-252 + 6c + 6c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-42 + c + c2) = 0

Factor a trinomial.
6((-7 + -1c)(6 + -1c)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-7 + -1c)' equal to zero and attempt to solve:

Simplifying
-7 + -1c = 0

Solving
-7 + -1c = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1c = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1c = 0 + 7
-1c = 0 + 7

Combine like terms: 0 + 7 = 7
-1c = 7

Divide each side by '-1'.
c = -7

Simplifying
c = -7
Subproblem 2
Set the factor '(6 + -1c)' equal to zero and attempt to solve:

Simplifying
6 + -1c = 0

Solving
6 + -1c = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1c = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1c = 0 + -6
-1c = 0 + -6

Combine like terms: 0 + -6 = -6
-1c = -6

Divide each side by '-1'.
c = 6

Simplifying
c = 6
Solution
c = {-7, 6}