z^6-4z^3=5z^3-20

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Solution for z^6-4z^3=5z^3-20 equation: 


Simplifying
z6 + -4z3 = 5z3 + -20

Reorder the terms:
-4z3 + z6 = 5z3 + -20

Reorder the terms:
-4z3 + z6 = -20 + 5z3

Solving
-4z3 + z6 = -20 + 5z3

Solving for variable 'z'.

Reorder the terms:
20 + -4z3 + -5z3 + z6 = -20 + 5z3 + 20 + -5z3

Combine like terms: -4z3 + -5z3 = -9z3
20 + -9z3 + z6 = -20 + 5z3 + 20 + -5z3

Reorder the terms:
20 + -9z3 + z6 = -20 + 20 + 5z3 + -5z3

Combine like terms: -20 + 20 = 0
20 + -9z3 + z6 = 0 + 5z3 + -5z3
20 + -9z3 + z6 = 5z3 + -5z3

Combine like terms: 5z3 + -5z3 = 0
20 + -9z3 + z6 = 0

Factor a trinomial.
(4 + -1z3)(5 + -1z3) = 0


Subproblem 1
Set the factor '(4 + -1z3)' equal to zero and attempt to solve:

Simplifying
4 + -1z3 = 0

Solving
4 + -1z3 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z3 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z3 = 0 + -4
-1z3 = 0 + -4

Combine like terms: 0 + -4 = -4
-1z3 = -4

Divide each side by '-1'.
z3 = 4

Simplifying
z3 = 4

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 '(5 + -1z3)' equal to zero and attempt to solve:

Simplifying
5 + -1z3 = 0

Solving
5 + -1z3 = 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 + -1z3 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z3 = 0 + -5
-1z3 = 0 + -5

Combine like terms: 0 + -5 = -5
-1z3 = -5

Divide each side by '-1'.
z3 = 5

Simplifying
z3 = 5

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.

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