c(c+4)+3c+12=0

Solution for c(c+4)+3c+12=0 equation:

Simplifying
c(c + 4) + 3c + 12 = 0

Reorder the terms:
c(4 + c) + 3c + 12 = 0
(4 * c + c * c) + 3c + 12 = 0
(4c + c2) + 3c + 12 = 0

Reorder the terms:
12 + 4c + 3c + c2 = 0

Combine like terms: 4c + 3c = 7c
12 + 7c + c2 = 0

Solving
12 + 7c + c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(4 + c)(3 + c) = 0

Subproblem 1
Set the factor '(4 + c)' equal to zero and attempt to solve:

Simplifying
4 + c = 0

Solving
4 + c = 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 + c = 0 + -4

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

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

Simplifying
c = -4
Subproblem 2
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
Solution
c = {-4, -3}