7c^2+105c+378=

Solution for 7c^2+105c+378= equation:

Simplifying
7c2 + 105c + 378 = 0

Reorder the terms:
378 + 105c + 7c2 = 0

Solving
378 + 105c + 7c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '7'.
7(54 + 15c + c2) = 0

Factor a trinomial.
7((9 + c)(6 + c)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(9 + c)' equal to zero and attempt to solve:

Simplifying
9 + c = 0

Solving
9 + c = 0

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

Add '-9' to each side of the equation.
9 + -9 + c = 0 + -9

Combine like terms: 9 + -9 = 0
0 + c = 0 + -9
c = 0 + -9

Combine like terms: 0 + -9 = -9
c = -9

Simplifying
c = -9
Subproblem 2
Set the factor '(6 + c)' equal to zero and attempt to solve:

Simplifying
6 + c = 0

Solving
6 + c = 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 + c = 0 + -6

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

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

Simplifying
c = -6
Solution
c = {-9, -6}