c(3c+4)+6(3c+4)=

Solution for c(3c+4)+6(3c+4)= equation:

Simplifying
c(3c + 4) + 6(3c + 4) = 0

Reorder the terms:
c(4 + 3c) + 6(3c + 4) = 0
(4 * c + 3c * c) + 6(3c + 4) = 0
(4c + 3c2) + 6(3c + 4) = 0

Reorder the terms:
4c + 3c2 + 6(4 + 3c) = 0
4c + 3c2 + (4 * 6 + 3c * 6) = 0
4c + 3c2 + (24 + 18c) = 0

Reorder the terms:
24 + 4c + 18c + 3c2 = 0

Combine like terms: 4c + 18c = 22c
24 + 22c + 3c2 = 0

Solving
24 + 22c + 3c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(6 + c)(4 + 3c) = 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 '(4 + 3c)' equal to zero and attempt to solve:

Simplifying
4 + 3c = 0

Solving
4 + 3c = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3c = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3c = 0 + -4
3c = 0 + -4

Combine like terms: 0 + -4 = -4
3c = -4

Divide each side by '3'.
c = -1.333333333

Simplifying
c = -1.333333333
Solution
c = {-6, -1.333333333}