z^4+3z^2=10

Solution for z^4+3z^2=10 equation:

Simplifying
z4 + 3z2 = 10

Reorder the terms:
3z2 + z4 = 10

Solving
3z2 + z4 = 10

Solving for variable 'z'.

Reorder the terms:
-10 + 3z2 + z4 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 3z2 + z4 = 0

Factor a trinomial.
(-5 + -1z2)(2 + -1z2) = 0

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

Simplifying
-5 + -1z2 = 0

Solving
-5 + -1z2 = 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 + -1z2 = 0 + 5

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

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

Divide each side by '-1'.
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 '(2 + -1z2)' equal to zero and attempt to solve:

Simplifying
2 + -1z2 = 0

Solving
2 + -1z2 = 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 + -1z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z2 = 0 + -2
-1z2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1z2 = -2

Divide each side by '-1'.
z2 = 2

Simplifying
z2 = 2

Take the square root of each side:
z = {-1.414213562, 1.414213562}
Solution
z = {-1.414213562, 1.414213562}