-3(z^2-4z-12)=0

Solution for -3(z^2-4z-12)=0 equation:

Simplifying
-3(z2 + -4z + -12) = 0

Reorder the terms:
-3(-12 + -4z + z2) = 0
(-12 * -3 + -4z * -3 + z2 * -3) = 0
(36 + 12z + -3z2) = 0

Solving
36 + 12z + -3z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + 4z + -1z2) = 0

Factor a trinomial.
3((6 + -1z)(2 + z)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Subproblem 2
Set the factor '(2 + z)' equal to zero and attempt to solve:

Simplifying
2 + z = 0

Solving
2 + z = 0

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

Add '-2' to each side of the equation.
2 + -2 + z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + z = 0 + -2
z = 0 + -2

Combine like terms: 0 + -2 = -2
z = -2

Simplifying
z = -2
Solution
z = {6, -2}