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Simplifying -5z(z + -2)(z + 4) = 0 Reorder the terms: -5z(-2 + z)(z + 4) = 0 Reorder the terms: -5z(-2 + z)(4 + z) = 0 Multiply (-2 + z) * (4 + z) -5z(-2(4 + z) + z(4 + z)) = 0 -5z((4 * -2 + z * -2) + z(4 + z)) = 0 -5z((-8 + -2z) + z(4 + z)) = 0 -5z(-8 + -2z + (4 * z + z * z)) = 0 -5z(-8 + -2z + (4z + z2)) = 0 Combine like terms: -2z + 4z = 2z -5z(-8 + 2z + z2) = 0 (-8 * -5z + 2z * -5z + z2 * -5z) = 0 (40z + -10z2 + -5z3) = 0 Solving 40z + -10z2 + -5z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z'. 5z(8 + -2z + -1z2) = 0 Factor a trinomial. 5z((2 + -1z)(4 + z)) = 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 = 0Subproblem 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 = 2Subproblem 3
Set the factor '(4 + z)' equal to zero and attempt to solve: Simplifying 4 + z = 0 Solving 4 + z = 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 + z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + z = 0 + -4 z = 0 + -4 Combine like terms: 0 + -4 = -4 z = -4 Simplifying z = -4Solution
z = {0, 2, -4}
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