6z^3+36z^2=162z

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Solution for 6z^3+36z^2=162z equation:


Simplifying
6z3 + 36z2 = 162z

Reorder the terms:
36z2 + 6z3 = 162z

Solving
36z2 + 6z3 = 162z

Solving for variable 'z'.

Reorder the terms:
-162z + 36z2 + 6z3 = 162z + -162z

Combine like terms: 162z + -162z = 0
-162z + 36z2 + 6z3 = 0

Factor out the Greatest Common Factor (GCF), '6z'.
6z(-27 + 6z + z2) = 0

Factor a trinomial.
6z((-9 + -1z)(3 + -1z)) = 0

Ignore the factor 6.

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 '(-9 + -1z)' equal to zero and attempt to solve: Simplifying -9 + -1z = 0 Solving -9 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1z = 0 + 9 -1z = 0 + 9 Combine like terms: 0 + 9 = 9 -1z = 9 Divide each side by '-1'. z = -9 Simplifying z = -9

Subproblem 3

Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3

Solution

z = {0, -9, 3}

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