c^2d^2+7cd+12=0

Solution for c^2d^2+7cd+12=0 equation:

Simplifying
c2d2 + 7cd + 12 = 0

Reorder the terms:
12 + 7cd + c2d2 = 0

Solving
12 + 7cd + c2d2 = 0

Solving for variable 'c'.

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

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

Simplifying
4 + cd = 0

Solving
4 + cd = 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 + cd = 0 + -4

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

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

Divide each side by 'd'.
c = -4d-1

Simplifying
c = -4d-1
Subproblem 2
Set the factor '(3 + cd)' equal to zero and attempt to solve:

Simplifying
3 + cd = 0

Solving
3 + cd = 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 + cd = 0 + -3

Combine like terms: 3 + -3 = 0
0 + cd = 0 + -3
cd = 0 + -3

Combine like terms: 0 + -3 = -3
cd = -3

Divide each side by 'd'.
c = -3d-1

Simplifying
c = -3d-1
Solution
c = {-4d-1, -3d-1}