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

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

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

Reorder the terms:
c(3 + 2c) + 6(2c + 3) = 0
(3 * c + 2c * c) + 6(2c + 3) = 0
(3c + 2c2) + 6(2c + 3) = 0

Reorder the terms:
3c + 2c2 + 6(3 + 2c) = 0
3c + 2c2 + (3 * 6 + 2c * 6) = 0
3c + 2c2 + (18 + 12c) = 0

Reorder the terms:
18 + 3c + 12c + 2c2 = 0

Combine like terms: 3c + 12c = 15c
18 + 15c + 2c2 = 0

Solving
18 + 15c + 2c2 = 0

Solving for variable 'c'.

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

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

Simplifying
3 + 2c = 0

Solving
3 + 2c = 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 + 2c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2c = 0 + -3
2c = 0 + -3

Combine like terms: 0 + -3 = -3
2c = -3

Divide each side by '2'.
c = -1.5

Simplifying
c = -1.5
Solution
c = {-6, -1.5}