64z^3-32z^2-12z=0

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Solution for 64z^3-32z^2-12z=0 equation:


Simplifying
64z3 + -32z2 + -12z = 0

Reorder the terms:
-12z + -32z2 + 64z3 = 0

Solving
-12z + -32z2 + 64z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z'.
4z(-3 + -8z + 16z2) = 0

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

Ignore the factor 4.

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 '(-1 + -4z)' equal to zero and attempt to solve: Simplifying -1 + -4z = 0 Solving -1 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4z = 0 + 1 -4z = 0 + 1 Combine like terms: 0 + 1 = 1 -4z = 1 Divide each side by '-4'. z = -0.25 Simplifying z = -0.25

Subproblem 3

Set the factor '(3 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 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 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Divide each side by '-4'. z = 0.75 Simplifying z = 0.75

Solution

z = {0, -0.25, 0.75}

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