2z^4-19z^2=10

Solution for 2z^4-19z^2=10 equation:

Simplifying
2z4 + -19z2 = 10

Reorder the terms:
-19z2 + 2z4 = 10

Solving
-19z2 + 2z4 = 10

Solving for variable 'z'.

Reorder the terms:
-10 + -19z2 + 2z4 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -19z2 + 2z4 = 0

Factor a trinomial.
(-1 + -2z2)(10 + -1z2) = 0

Subproblem 1
Set the factor '(-1 + -2z2)' equal to zero and attempt to solve:

Simplifying
-1 + -2z2 = 0

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

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

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

Divide each side by '-2'.
z2 = -0.5

Simplifying
z2 = -0.5

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 '(10 + -1z2)' equal to zero and attempt to solve:

Simplifying
10 + -1z2 = 0

Solving
10 + -1z2 = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1z2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1z2 = 0 + -10
-1z2 = 0 + -10

Combine like terms: 0 + -10 = -10
-1z2 = -10

Divide each side by '-1'.
z2 = 10

Simplifying
z2 = 10

Take the square root of each side:
z = {-3.16227766, 3.16227766}
Solution
z = {-3.16227766, 3.16227766}