-4z(z-1)(z-8)=0

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Solution for -4z(z-1)(z-8)=0 equation:


Simplifying
-4z(z + -1)(z + -8) = 0

Reorder the terms:
-4z(-1 + z)(z + -8) = 0

Reorder the terms:
-4z(-1 + z)(-8 + z) = 0

Multiply (-1 + z) * (-8 + z)
-4z(-1(-8 + z) + z(-8 + z)) = 0
-4z((-8 * -1 + z * -1) + z(-8 + z)) = 0
-4z((8 + -1z) + z(-8 + z)) = 0
-4z(8 + -1z + (-8 * z + z * z)) = 0
-4z(8 + -1z + (-8z + z2)) = 0

Combine like terms: -1z + -8z = -9z
-4z(8 + -9z + z2) = 0
(8 * -4z + -9z * -4z + z2 * -4z) = 0
(-32z + 36z2 + -4z3) = 0

Solving
-32z + 36z2 + -4z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z'.
4z(-8 + 9z + -1z2) = 0

Factor a trinomial.
4z((-8 + z)(1 + -1z)) = 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 '(-8 + z)' equal to zero and attempt to solve: Simplifying -8 + z = 0 Solving -8 + z = 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 + z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + z = 0 + 8 z = 0 + 8 Combine like terms: 0 + 8 = 8 z = 8 Simplifying z = 8

Subproblem 3

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

Solution

z = {0, 8, 1}

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