(2c+6)(3c+6)=0

Solution for (2c+6)(3c+6)=0 equation:

Simplifying
(2c + 6)(3c + 6) = 0

Reorder the terms:
(6 + 2c)(3c + 6) = 0

Reorder the terms:
(6 + 2c)(6 + 3c) = 0

Multiply (6 + 2c) * (6 + 3c)
(6(6 + 3c) + 2c * (6 + 3c)) = 0
((6 * 6 + 3c * 6) + 2c * (6 + 3c)) = 0
((36 + 18c) + 2c * (6 + 3c)) = 0
(36 + 18c + (6 * 2c + 3c * 2c)) = 0
(36 + 18c + (12c + 6c2)) = 0

Combine like terms: 18c + 12c = 30c
(36 + 30c + 6c2) = 0

Solving
36 + 30c + 6c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + 5c + c2) = 0

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

Ignore the factor 6.
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 '(2 + c)' equal to zero and attempt to solve:

Simplifying
2 + c = 0

Solving
2 + c = 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 + c = 0 + -2

Combine like terms: 2 + -2 = 0
0 + c = 0 + -2
c = 0 + -2

Combine like terms: 0 + -2 = -2
c = -2

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