(4z^4)-25=0

Solution for (4z^4)-25=0 equation:

Simplifying
(4z4) + -25 = 0

Reorder the terms:
-25 + (4z4) = 0

Solving
-25 + (4z4) = 0

Solving for variable 'z'.

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

Add '25' to each side of the equation.
-25 + 25 + (4z4) = 0 + 25

Combine like terms: -25 + 25 = 0
0 + (4z4) = 0 + 25
(4z4) = 0 + 25

Combine like terms: 0 + 25 = 25
(4z4) = 25

Divide each side by '4'.
z4 = 6.25

Simplifying
z4 = 6.25

Reorder the terms:
-6.25 + z4 = 6.25 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
-6.25 + z4 = 0.00

Factor a difference between two squares.
(2.5 + z2)(-2.5 + z2) = 0.00

Subproblem 1
Set the factor '(2.5 + z2)' equal to zero and attempt to solve:

Simplifying
2.5 + z2 = 0

Solving
2.5 + z2 = 0

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + z2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + z2 = 0 + -2.5
z2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
z2 = -2.5

Simplifying
z2 = -2.5

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 '(-2.5 + z2)' equal to zero and attempt to solve:

Simplifying
-2.5 + z2 = 0

Solving
-2.5 + z2 = 0

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + z2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + z2 = 0 + 2.5
z2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
z2 = 2.5

Simplifying
z2 = 2.5

Take the square root of each side:
z = {-1.58113883, 1.58113883}
Solution
z = {-1.58113883, 1.58113883}