(3z^4+8z^2-21)-(2z^4+11z^2-4)=0

Solution for (3z^4+8z^2-21)-(2z^4+11z^2-4)=0 equation:

Simplifying
(3z4 + 8z2 + -21) + -1(2z4 + 11z2 + -4) = 0

Reorder the terms:
(-21 + 8z2 + 3z4) + -1(2z4 + 11z2 + -4) = 0

Remove parenthesis around (-21 + 8z2 + 3z4)
-21 + 8z2 + 3z4 + -1(2z4 + 11z2 + -4) = 0

Reorder the terms:
-21 + 8z2 + 3z4 + -1(-4 + 11z2 + 2z4) = 0
-21 + 8z2 + 3z4 + (-4 * -1 + 11z2 * -1 + 2z4 * -1) = 0
-21 + 8z2 + 3z4 + (4 + -11z2 + -2z4) = 0

Reorder the terms:
-21 + 4 + 8z2 + -11z2 + 3z4 + -2z4 = 0

Combine like terms: -21 + 4 = -17
-17 + 8z2 + -11z2 + 3z4 + -2z4 = 0

Combine like terms: 8z2 + -11z2 = -3z2
-17 + -3z2 + 3z4 + -2z4 = 0

Combine like terms: 3z4 + -2z4 = 1z4
-17 + -3z2 + 1z4 = 0

Solving
-17 + -3z2 + 1z4 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -3z2 + 17 + z4 = 0 + 17

Reorder the terms:
-17 + 17 + -3z2 + z4 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -3z2 + z4 = 0 + 17
-3z2 + z4 = 0 + 17

Combine like terms: 0 + 17 = 17
-3z2 + z4 = 17

The z term is -3z2.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3z2 + 2.25 + z4 = 17 + 2.25

Reorder the terms:
2.25 + -3z2 + z4 = 17 + 2.25

Combine like terms: 17 + 2.25 = 19.25
2.25 + -3z2 + z4 = 19.25

Factor a perfect square on the left side:
(z2 + -1.5)(z2 + -1.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(z2 + -1.5) equal to 4.387482194 and -4.387482194.

Subproblem 1
z2 + -1.5 = 4.387482194

Simplifying
z2 + -1.5 = 4.387482194

Reorder the terms:
-1.5 + z2 = 4.387482194

Solving
-1.5 + z2 = 4.387482194

Solving for variable 'z'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + z2 = 4.387482194 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + z2 = 4.387482194 + 1.5
z2 = 4.387482194 + 1.5

Combine like terms: 4.387482194 + 1.5 = 5.887482194
z2 = 5.887482194

Simplifying
z2 = 5.887482194

Take the square root of each side:
z = {-2.426413443, 2.426413443}

Subproblem 2
z2 + -1.5 = -4.387482194

Simplifying
z2 + -1.5 = -4.387482194

Reorder the terms:
-1.5 + z2 = -4.387482194

Solving
-1.5 + z2 = -4.387482194

Solving for variable 'z'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + z2 = -4.387482194 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + z2 = -4.387482194 + 1.5
z2 = -4.387482194 + 1.5

Combine like terms: -4.387482194 + 1.5 = -2.887482194
z2 = -2.887482194

Simplifying
z2 = -2.887482194

Reorder the terms:
2.887482194 + z2 = -2.887482194 + 2.887482194

Combine like terms: -2.887482194 + 2.887482194 = 0.000000000
2.887482194 + z2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.