4*z^4=11*z^2+3

Solution for 4*z^4=11*z^2+3 equation:

Simplifying
4z4 = 11z2 + 3

Reorder the terms:
4z4 = 3 + 11z2

Solving
4z4 = 3 + 11z2

Solving for variable 'z'.

Reorder the terms:
-3 + -11z2 + 4z4 = 3 + 11z2 + -3 + -11z2

Reorder the terms:
-3 + -11z2 + 4z4 = 3 + -3 + 11z2 + -11z2

Combine like terms: 3 + -3 = 0
-3 + -11z2 + 4z4 = 0 + 11z2 + -11z2
-3 + -11z2 + 4z4 = 11z2 + -11z2

Combine like terms: 11z2 + -11z2 = 0
-3 + -11z2 + 4z4 = 0

Factor a trinomial.
(-1 + -4z2)(3 + -1z2) = 0

Subproblem 1
Set the factor '(-1 + -4z2)' equal to zero and attempt to solve:

Simplifying
-1 + -4z2 = 0

Solving
-1 + -4z2 = 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 + -4z2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4z2 = 0 + 1
-4z2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4z2 = 1

Divide each side by '-4'.
z2 = -0.25

Simplifying
z2 = -0.25

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 '(3 + -1z2)' equal to zero and attempt to solve:

Simplifying
3 + -1z2 = 0

Solving
3 + -1z2 = 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 + -1z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z2 = 0 + -3
-1z2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1z2 = -3

Divide each side by '-1'.
z2 = 3

Simplifying
z2 = 3

Take the square root of each side:
z = {-1.732050808, 1.732050808}
Solution
z = {-1.732050808, 1.732050808}