25z^4-20z^2+3=0

Solution for 25z^4-20z^2+3=0 equation:

Simplifying
25z4 + -20z2 + 3 = 0

Reorder the terms:
3 + -20z2 + 25z4 = 0

Solving
3 + -20z2 + 25z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -5z2)(3 + -5z2) = 0

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

Simplifying
1 + -5z2 = 0

Solving
1 + -5z2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5z2 = 0 + -1
-5z2 = 0 + -1

Combine like terms: 0 + -1 = -1
-5z2 = -1

Divide each side by '-5'.
z2 = 0.2

Simplifying
z2 = 0.2

Take the square root of each side:
z = {-0.447213596, 0.447213596}
Subproblem 2
Set the factor '(3 + -5z2)' equal to zero and attempt to solve:

Simplifying
3 + -5z2 = 0

Solving
3 + -5z2 = 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 + -5z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5z2 = 0 + -3
-5z2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5z2 = -3

Divide each side by '-5'.
z2 = 0.6

Simplifying
z2 = 0.6

Take the square root of each side:
z = {-0.774596669, 0.774596669}
Solution
z = {-0.447213596, 0.447213596, -0.774596669, 0.774596669}