80z^3+40z^2-75z=0

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Solution for 80z^3+40z^2-75z=0 equation:


Simplifying
80z3 + 40z2 + -75z = 0

Reorder the terms:
-75z + 40z2 + 80z3 = 0

Solving
-75z + 40z2 + 80z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '5z'.
5z(-15 + 8z + 16z2) = 0

Factor a trinomial.
5z((-5 + -4z)(3 + -4z)) = 0

Ignore the factor 5.

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 '(-5 + -4z)' equal to zero and attempt to solve: Simplifying -5 + -4z = 0 Solving -5 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -4z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4z = 0 + 5 -4z = 0 + 5 Combine like terms: 0 + 5 = 5 -4z = 5 Divide each side by '-4'. z = -1.25 Simplifying z = -1.25

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, -1.25, 0.75}

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