5z^4+10z^2=54-11z^2

Solution for 5z^4+10z^2=54-11z^2 equation:

Simplifying
5z4 + 10z2 = 54 + -11z2

Reorder the terms:
10z2 + 5z4 = 54 + -11z2

Solving
10z2 + 5z4 = 54 + -11z2

Solving for variable 'z'.

Reorder the terms:
-54 + 10z2 + 11z2 + 5z4 = 54 + -11z2 + -54 + 11z2

Combine like terms: 10z2 + 11z2 = 21z2
-54 + 21z2 + 5z4 = 54 + -11z2 + -54 + 11z2

Reorder the terms:
-54 + 21z2 + 5z4 = 54 + -54 + -11z2 + 11z2

Combine like terms: 54 + -54 = 0
-54 + 21z2 + 5z4 = 0 + -11z2 + 11z2
-54 + 21z2 + 5z4 = -11z2 + 11z2

Combine like terms: -11z2 + 11z2 = 0
-54 + 21z2 + 5z4 = 0

Factor a trinomial.
(-6 + -1z2)(9 + -5z2) = 0

Subproblem 1
Set the factor '(-6 + -1z2)' equal to zero and attempt to solve:

Simplifying
-6 + -1z2 = 0

Solving
-6 + -1z2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1z2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1z2 = 0 + 6
-1z2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1z2 = 6

Divide each side by '-1'.
z2 = -6

Simplifying
z2 = -6

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 '(9 + -5z2)' equal to zero and attempt to solve:

Simplifying
9 + -5z2 = 0

Solving
9 + -5z2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5z2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5z2 = 0 + -9
-5z2 = 0 + -9

Combine like terms: 0 + -9 = -9
-5z2 = -9

Divide each side by '-5'.
z2 = 1.8

Simplifying
z2 = 1.8

Take the square root of each side:
z = {-1.341640787, 1.341640787}
Solution
z = {-1.341640787, 1.341640787}