z(2z-9)(z+4)=0

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Solution for z(2z-9)(z+4)=0 equation:


Simplifying
z(2z + -9)(z + 4) = 0

Reorder the terms:
z(-9 + 2z)(z + 4) = 0

Reorder the terms:
z(-9 + 2z)(4 + z) = 0

Multiply (-9 + 2z) * (4 + z)
z(-9(4 + z) + 2z * (4 + z)) = 0
z((4 * -9 + z * -9) + 2z * (4 + z)) = 0
z((-36 + -9z) + 2z * (4 + z)) = 0
z(-36 + -9z + (4 * 2z + z * 2z)) = 0
z(-36 + -9z + (8z + 2z2)) = 0

Combine like terms: -9z + 8z = -1z
z(-36 + -1z + 2z2) = 0
(-36 * z + -1z * z + 2z2 * z) = 0
(-36z + -1z2 + 2z3) = 0

Solving
-36z + -1z2 + 2z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-36 + -1z + 2z2) = 0

Factor a trinomial.
z((-4 + -1z)(9 + -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 '(9 + -2z)' equal to zero and attempt to solve: Simplifying 9 + -2z = 0 Solving 9 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2z = 0 + -9 -2z = 0 + -9 Combine like terms: 0 + -9 = -9 -2z = -9 Divide each side by '-2'. z = 4.5 Simplifying z = 4.5

Solution

z = {0, -4, 4.5}

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