6z^4-150=0

Solution for 6z^4-150=0 equation:

Simplifying
6z4 + -150 = 0

Reorder the terms:
-150 + 6z4 = 0

Solving
-150 + 6z4 = 0

Solving for variable 'z'.

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

Add '150' to each side of the equation.
-150 + 150 + 6z4 = 0 + 150

Combine like terms: -150 + 150 = 0
0 + 6z4 = 0 + 150
6z4 = 0 + 150

Combine like terms: 0 + 150 = 150
6z4 = 150

Divide each side by '6'.
z4 = 25

Simplifying
z4 = 25

Reorder the terms:
-25 + z4 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + z4 = 0

Factor a difference between two squares.
(5 + z2)(-5 + z2) = 0

Subproblem 1
Set the factor '(5 + z2)' equal to zero and attempt to solve:

Simplifying
5 + z2 = 0

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

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

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

Simplifying
z2 = -5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-5 + z2)' equal to zero and attempt to solve:

Simplifying
-5 + z2 = 0

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

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

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

Simplifying
z2 = 5

Take the square root of each side:
z = {-2.236067978, 2.236067978}
Solution
z = {-2.236067978, 2.236067978}