(5c+3)(2c+6)=0

Solution for (5c+3)(2c+6)=0 equation:

Simplifying
(5c + 3)(2c + 6) = 0

Reorder the terms:
(3 + 5c)(2c + 6) = 0

Reorder the terms:
(3 + 5c)(6 + 2c) = 0

Multiply (3 + 5c) * (6 + 2c)
(3(6 + 2c) + 5c * (6 + 2c)) = 0
((6 * 3 + 2c * 3) + 5c * (6 + 2c)) = 0
((18 + 6c) + 5c * (6 + 2c)) = 0
(18 + 6c + (6 * 5c + 2c * 5c)) = 0
(18 + 6c + (30c + 10c2)) = 0

Combine like terms: 6c + 30c = 36c
(18 + 36c + 10c2) = 0

Solving
18 + 36c + 10c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 18c + 5c2) = 0

Factor a trinomial.
2((3 + c)(3 + 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 '(3 + 5c)' equal to zero and attempt to solve:

Simplifying
3 + 5c = 0

Solving
3 + 5c = 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 + 5c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5c = 0 + -3
5c = 0 + -3

Combine like terms: 0 + -3 = -3
5c = -3

Divide each side by '5'.
c = -0.6

Simplifying
c = -0.6
Solution
c = {-3, -0.6}