z^3-36z=0

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Solution for z^3-36z=0 equation:


Simplifying
z3 + -36z = 0

Reorder the terms:
-36z + z3 = 0

Solving
-36z + z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-36 + z2) = 0

Factor a difference between two squares.
z((6 + z)(-6 + z)) = 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 '(6 + z)' equal to zero and attempt to solve: Simplifying 6 + z = 0 Solving 6 + z = 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 + z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + z = 0 + -6 z = 0 + -6 Combine like terms: 0 + -6 = -6 z = -6 Simplifying z = -6

Subproblem 3

Set the factor '(-6 + z)' equal to zero and attempt to solve: Simplifying -6 + z = 0 Solving -6 + z = 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 + z = 0 + 6 Combine like terms: -6 + 6 = 0 0 + z = 0 + 6 z = 0 + 6 Combine like terms: 0 + 6 = 6 z = 6 Simplifying z = 6

Solution

z = {0, -6, 6}

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