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Simplifying -4z(z + -2)(z + 9) = 0 Reorder the terms: -4z(-2 + z)(z + 9) = 0 Reorder the terms: -4z(-2 + z)(9 + z) = 0 Multiply (-2 + z) * (9 + z) -4z(-2(9 + z) + z(9 + z)) = 0 -4z((9 * -2 + z * -2) + z(9 + z)) = 0 -4z((-18 + -2z) + z(9 + z)) = 0 -4z(-18 + -2z + (9 * z + z * z)) = 0 -4z(-18 + -2z + (9z + z2)) = 0 Combine like terms: -2z + 9z = 7z -4z(-18 + 7z + z2) = 0 (-18 * -4z + 7z * -4z + z2 * -4z) = 0 (72z + -28z2 + -4z3) = 0 Solving 72z + -28z2 + -4z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4z'. 4z(18 + -7z + -1z2) = 0 Factor a trinomial. 4z((2 + -1z)(9 + z)) = 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 '(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 '(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 = -9Solution
z = {0, 2, -9}
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