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Simplifying -4z(z + -2)(z + -4) = 0 Reorder the terms: -4z(-2 + z)(z + -4) = 0 Reorder the terms: -4z(-2 + z)(-4 + z) = 0 Multiply (-2 + z) * (-4 + z) -4z(-2(-4 + z) + z(-4 + z)) = 0 -4z((-4 * -2 + z * -2) + z(-4 + z)) = 0 -4z((8 + -2z) + z(-4 + z)) = 0 -4z(8 + -2z + (-4 * z + z * z)) = 0 -4z(8 + -2z + (-4z + z2)) = 0 Combine like terms: -2z + -4z = -6z -4z(8 + -6z + z2) = 0 (8 * -4z + -6z * -4z + z2 * -4z) = 0 (-32z + 24z2 + -4z3) = 0 Solving -32z + 24z2 + -4z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4z'. 4z(-8 + 6z + -1z2) = 0 Factor a trinomial. 4z((-4 + z)(2 + -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 = 0Subproblem 2
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 = 4Subproblem 3
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 = 2Solution
z = {0, 4, 2}
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