12z^2+72z+108=0

Solution for 12z^2+72z+108=0 equation:

Simplifying
12z2 + 72z + 108 = 0

Reorder the terms:
108 + 72z + 12z2 = 0

Solving
108 + 72z + 12z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '12'.
12(9 + 6z + z2) = 0

Factor a trinomial.
12((3 + z)(3 + z)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 0

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

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

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

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

Simplifying
z = -3
Subproblem 2
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 0

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

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

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

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

Simplifying
z = -3
Solution
z = {-3, -3}