Z^2(4z^4+z^3-11z^2-6)=

Solution for Z^2(4z^4+z^3-11z^2-6)= equation:

Simplifying
Z2(4z4 + z3 + -11z2 + -6) = 0

Reorder the terms:
Z2(-6 + -11z2 + z3 + 4z4) = 0
(-6 * Z2 + -11z2 * Z2 + z3 * Z2 + 4z4 * Z2) = 0
(-6Z2 + -11z2Z2 + z3Z2 + 4z4Z2) = 0

Solving
-6Z2 + -11z2Z2 + z3Z2 + 4z4Z2 = 0

Solving for variable 'Z'.

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

Factor out the Greatest Common Factor (GCF), 'Z2'.
Z2(-6 + -11z2 + z3 + 4z4) = 0

Subproblem 1
Set the factor 'Z2' equal to zero and attempt to solve:

Simplifying
Z2 = 0

Solving
Z2 = 0

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

Simplifying
Z2 = 0

Take the square root of each side:
Z = {0}
Subproblem 2
Set the factor '(-6 + -11z2 + z3 + 4z4)' equal to zero and attempt to solve:

Simplifying
-6 + -11z2 + z3 + 4z4 = 0

Solving
-6 + -11z2 + z3 + 4z4 = 0

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

Add '6' to each side of the equation.
-6 + -11z2 + z3 + 6 + 4z4 = 0 + 6

Reorder the terms:
-6 + 6 + -11z2 + z3 + 4z4 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -11z2 + z3 + 4z4 = 0 + 6
-11z2 + z3 + 4z4 = 0 + 6

Combine like terms: 0 + 6 = 6
-11z2 + z3 + 4z4 = 6

Add '11z2' to each side of the equation.
-11z2 + z3 + 11z2 + 4z4 = 6 + 11z2

Reorder the terms:
-11z2 + 11z2 + z3 + 4z4 = 6 + 11z2

Combine like terms: -11z2 + 11z2 = 0
0 + z3 + 4z4 = 6 + 11z2
z3 + 4z4 = 6 + 11z2

Add '-1z3' to each side of the equation.
z3 + -1z3 + 4z4 = 6 + 11z2 + -1z3

Combine like terms: z3 + -1z3 = 0
0 + 4z4 = 6 + 11z2 + -1z3
4z4 = 6 + 11z2 + -1z3

Add '-4z4' to each side of the equation.
4z4 + -4z4 = 6 + 11z2 + -1z3 + -4z4

Combine like terms: 4z4 + -4z4 = 0
0 = 6 + 11z2 + -1z3 + -4z4

Simplifying
0 = 6 + 11z2 + -1z3 + -4z4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
Z = {0}