60z^2-9z-27=0

Solution for 60z^2-9z-27=0 equation:

Simplifying
60z2 + -9z + -27 = 0

Reorder the terms:
-27 + -9z + 60z2 = 0

Solving
-27 + -9z + 60z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -3z + 20z2) = 0

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

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

Simplifying
-3 + -5z = 0

Solving
-3 + -5z = 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 + -5z = 0 + 3

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

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

Divide each side by '-5'.
z = -0.6

Simplifying
z = -0.6
Subproblem 2
Set the factor '(3 + -4z)' equal to zero and attempt to solve:

Simplifying
3 + -4z = 0

Solving
3 + -4z = 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 + -4z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4z = 0 + -3
-4z = 0 + -3

Combine like terms: 0 + -3 = -3
-4z = -3

Divide each side by '-4'.
z = 0.75

Simplifying
z = 0.75
Solution
z = {-0.6, 0.75}