30z^6-33z^4-18z^2=

Solution for 30z^6-33z^4-18z^2= equation:

Simplifying
30z6 + -33z4 + -18z2 = 0

Reorder the terms:
-18z2 + -33z4 + 30z6 = 0

Solving
-18z2 + -33z4 + 30z6 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z2'.
3z2(-6 + -11z2 + 10z4) = 0

Factor a trinomial.
3z2((-2 + -5z2)(3 + -2z2)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

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

Simplifying
z2 = 0

Take the square root of each side:
z = {0}
Subproblem 2
Set the factor '(-2 + -5z2)' equal to zero and attempt to solve:

Simplifying
-2 + -5z2 = 0

Solving
-2 + -5z2 = 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 + -5z2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5z2 = 0 + 2
-5z2 = 0 + 2

Combine like terms: 0 + 2 = 2
-5z2 = 2

Divide each side by '-5'.
z2 = -0.4

Simplifying
z2 = -0.4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(3 + -2z2)' equal to zero and attempt to solve:

Simplifying
3 + -2z2 = 0

Solving
3 + -2z2 = 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 + -2z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2z2 = 0 + -3
-2z2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2z2 = -3

Divide each side by '-2'.
z2 = 1.5

Simplifying
z2 = 1.5

Take the square root of each side:
z = {-1.224744871, 1.224744871}
Solution
z = {0, -1.224744871, 1.224744871}