5z^4+9z^2-80=0

Solution for 5z^4+9z^2-80=0 equation:

Simplifying
5z4 + 9z2 + -80 = 0

Reorder the terms:
-80 + 9z2 + 5z4 = 0

Solving
-80 + 9z2 + 5z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(-5 + -1z2)(16 + -5z2) = 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 '(16 + -5z2)' equal to zero and attempt to solve:

Simplifying
16 + -5z2 = 0

Solving
16 + -5z2 = 0

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

Add '-16' to each side of the equation.
16 + -16 + -5z2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -5z2 = 0 + -16
-5z2 = 0 + -16

Combine like terms: 0 + -16 = -16
-5z2 = -16

Divide each side by '-5'.
z2 = 3.2

Simplifying
z2 = 3.2

Take the square root of each side:
z = {-1.788854382, 1.788854382}
Solution
z = {-1.788854382, 1.788854382}