2z^3-60z=2z^2

Solution for 2z^3-60z=2z^2 equation:

Simplifying
2z3 + -60z = 2z2

Reorder the terms:
-60z + 2z3 = 2z2

Solving
-60z + 2z3 = 2z2

Solving for variable 'z'.

Reorder the terms:
-60z + -2z2 + 2z3 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
-60z + -2z2 + 2z3 = 0

Factor out the Greatest Common Factor (GCF), '2z'.
2z(-30 + -1z + z2) = 0

Factor a trinomial.
2z((-5 + -1z)(6 + -1z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(-5 + -1z)' equal to zero and attempt to solve:

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 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 + -1z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1z = 0 + 5
-1z = 0 + 5

Combine like terms: 0 + 5 = 5
-1z = 5

Divide each side by '-1'.
z = -5

Simplifying
z = -5
Subproblem 3
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 = {0, -5, 6}