10z^4-27z^2+5=0

Solution for 10z^4-27z^2+5=0 equation:

Simplifying
10z4 + -27z2 + 5 = 0

Reorder the terms:
5 + -27z2 + 10z4 = 0

Solving
5 + -27z2 + 10z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -5z2)(5 + -2z2) = 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 '(5 + -2z2)' equal to zero and attempt to solve:

Simplifying
5 + -2z2 = 0

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

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

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

Divide each side by '-2'.
z2 = 2.5

Simplifying
z2 = 2.5

Take the square root of each side:
z = {-1.58113883, 1.58113883}
Solution
z = {-0.447213596, 0.447213596, -1.58113883, 1.58113883}