(z*z*z)-(z*z)=56z

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Solution for (z*z*z)-(z*z)=56z equation: 


Simplifying
(z * z * z) + -1(z * z) = 56z

Multiply z * z
(z2 * z) + -1(z * z) = 56z

Multiply z2 * z
(z3) + -1(z * z) = 56z
z3 + -1(z * z) = 56z

Multiply z * z
z3 + -1(z2) = 56z

Reorder the terms:
-1z2 + z3 = 56z

Solving
-1z2 + z3 = 56z

Solving for variable 'z'.

Reorder the terms:
-56z + -1z2 + z3 = 56z + -56z

Combine like terms: 56z + -56z = 0
-56z + -1z2 + z3 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(-56 + -1z + z2) = 0

Factor a trinomial.
z((-7 + -1z)(8 + -1z)) = 0


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

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0

Subproblem 2
Set the factor '(-7 + -1z)' equal to zero and attempt to solve:

Simplifying
-7 + -1z = 0

Solving
-7 + -1z = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1z = 0 + 7
-1z = 0 + 7

Combine like terms: 0 + 7 = 7
-1z = 7

Divide each side by '-1'.
z = -7

Simplifying
z = -7

Subproblem 3
Set the factor '(8 + -1z)' equal to zero and attempt to solve:

Simplifying
8 + -1z = 0

Solving
8 + -1z = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1z = 0 + -8
-1z = 0 + -8

Combine like terms: 0 + -8 = -8
-1z = -8

Divide each side by '-1'.
z = 8

Simplifying
z = 8
Solution
z = {0, -7, 8}

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