z(2z-5)(z+4)=0

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Solution for z(2z-5)(z+4)=0 equation:


Simplifying
z(2z + -5)(z + 4) = 0

Reorder the terms:
z(-5 + 2z)(z + 4) = 0

Reorder the terms:
z(-5 + 2z)(4 + z) = 0

Multiply (-5 + 2z) * (4 + z)
z(-5(4 + z) + 2z * (4 + z)) = 0
z((4 * -5 + z * -5) + 2z * (4 + z)) = 0
z((-20 + -5z) + 2z * (4 + z)) = 0
z(-20 + -5z + (4 * 2z + z * 2z)) = 0
z(-20 + -5z + (8z + 2z2)) = 0

Combine like terms: -5z + 8z = 3z
z(-20 + 3z + 2z2) = 0
(-20 * z + 3z * z + 2z2 * z) = 0
(-20z + 3z2 + 2z3) = 0

Solving
-20z + 3z2 + 2z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-20 + 3z + 2z2) = 0

Factor a trinomial.
z((-4 + -1z)(5 + -2z)) = 0

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

Subproblem 3

Set the factor '(5 + -2z)' equal to zero and attempt to solve: Simplifying 5 + -2z = 0 Solving 5 + -2z = 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 + -2z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2z = 0 + -5 -2z = 0 + -5 Combine like terms: 0 + -5 = -5 -2z = -5 Divide each side by '-2'. z = 2.5 Simplifying z = 2.5

Solution

z = {0, -4, 2.5}

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