10c^2+42c+36=0

Solution for 10c^2+42c+36=0 equation:

Simplifying
10c2 + 42c + 36 = 0

Reorder the terms:
36 + 42c + 10c2 = 0

Solving
36 + 42c + 10c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + 21c + 5c2) = 0

Factor a trinomial.
2((3 + c)(6 + 5c)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + c)' equal to zero and attempt to solve:

Simplifying
3 + c = 0

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

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

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

Simplifying
c = -3
Subproblem 2
Set the factor '(6 + 5c)' equal to zero and attempt to solve:

Simplifying
6 + 5c = 0

Solving
6 + 5c = 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 + 5c = 0 + -6

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

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

Divide each side by '5'.
c = -1.2

Simplifying
c = -1.2
Solution
c = {-3, -1.2}