5z(z+2)(z-1)=0

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Solution for 5z(z+2)(z-1)=0 equation:


Simplifying
5z(z + 2)(z + -1) = 0

Reorder the terms:
5z(2 + z)(z + -1) = 0

Reorder the terms:
5z(2 + z)(-1 + z) = 0

Multiply (2 + z) * (-1 + z)
5z(2(-1 + z) + z(-1 + z)) = 0
5z((-1 * 2 + z * 2) + z(-1 + z)) = 0
5z((-2 + 2z) + z(-1 + z)) = 0
5z(-2 + 2z + (-1 * z + z * z)) = 0
5z(-2 + 2z + (-1z + z2)) = 0

Combine like terms: 2z + -1z = 1z
5z(-2 + 1z + z2) = 0
(-2 * 5z + 1z * 5z + z2 * 5z) = 0
(-10z + 5z2 + 5z3) = 0

Solving
-10z + 5z2 + 5z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '5z'.
5z(-2 + z + z2) = 0

Factor a trinomial.
5z((-2 + -1z)(1 + -1z)) = 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 '(-2 + -1z)' equal to zero and attempt to solve: Simplifying -2 + -1z = 0 Solving -2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1z = 0 + 2 -1z = 0 + 2 Combine like terms: 0 + 2 = 2 -1z = 2 Divide each side by '-1'. z = -2 Simplifying z = -2

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, -2, 1}

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