12z^2-52z-120=0

Solution for 12z^2-52z-120=0 equation:

Simplifying
12z2 + -52z + -120 = 0

Reorder the terms:
-120 + -52z + 12z2 = 0

Solving
-120 + -52z + 12z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-30 + -13z + 3z2) = 0

Factor a trinomial.
4((-5 + -3z)(6 + -1z)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + -3z)' equal to zero and attempt to solve:

Simplifying
-5 + -3z = 0

Solving
-5 + -3z = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3z = 0 + 5
-3z = 0 + 5

Combine like terms: 0 + 5 = 5
-3z = 5

Divide each side by '-3'.
z = -1.666666667

Simplifying
z = -1.666666667
Subproblem 2
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
Solution
z = {-1.666666667, 6}