3z^3+12z^2=96z

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Solution for 3z^3+12z^2=96z equation:


Simplifying
3z3 + 12z2 = 96z

Reorder the terms:
12z2 + 3z3 = 96z

Solving
12z2 + 3z3 = 96z

Solving for variable 'z'.

Reorder the terms:
-96z + 12z2 + 3z3 = 96z + -96z

Combine like terms: 96z + -96z = 0
-96z + 12z2 + 3z3 = 0

Factor out the Greatest Common Factor (GCF), '3z'.
3z(-32 + 4z + z2) = 0

Factor a trinomial.
3z((-8 + -1z)(4 + -1z)) = 0

Ignore the factor 3.

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 '(-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

Subproblem 3

Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 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 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4

Solution

z = {0, -8, 4}

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