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Simplifying -4z(z + -3)(z + -9) = 0 Reorder the terms: -4z(-3 + z)(z + -9) = 0 Reorder the terms: -4z(-3 + z)(-9 + z) = 0 Multiply (-3 + z) * (-9 + z) -4z(-3(-9 + z) + z(-9 + z)) = 0 -4z((-9 * -3 + z * -3) + z(-9 + z)) = 0 -4z((27 + -3z) + z(-9 + z)) = 0 -4z(27 + -3z + (-9 * z + z * z)) = 0 -4z(27 + -3z + (-9z + z2)) = 0 Combine like terms: -3z + -9z = -12z -4z(27 + -12z + z2) = 0 (27 * -4z + -12z * -4z + z2 * -4z) = 0 (-108z + 48z2 + -4z3) = 0 Solving -108z + 48z2 + -4z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4z'. 4z(-27 + 12z + -1z2) = 0 Factor a trinomial. 4z((-9 + z)(3 + -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 '(-9 + z)' equal to zero and attempt to solve: Simplifying -9 + z = 0 Solving -9 + z = 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 + z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + z = 0 + 9 z = 0 + 9 Combine like terms: 0 + 9 = 9 z = 9 Simplifying z = 9Subproblem 3
Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Solution
z = {0, 9, 3}
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