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Simplifying -5z(z + 9)(z + 5) = 0 Reorder the terms: -5z(9 + z)(z + 5) = 0 Reorder the terms: -5z(9 + z)(5 + z) = 0 Multiply (9 + z) * (5 + z) -5z(9(5 + z) + z(5 + z)) = 0 -5z((5 * 9 + z * 9) + z(5 + z)) = 0 -5z((45 + 9z) + z(5 + z)) = 0 -5z(45 + 9z + (5 * z + z * z)) = 0 -5z(45 + 9z + (5z + z2)) = 0 Combine like terms: 9z + 5z = 14z -5z(45 + 14z + z2) = 0 (45 * -5z + 14z * -5z + z2 * -5z) = 0 (-225z + -70z2 + -5z3) = 0 Solving -225z + -70z2 + -5z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '-5z'. -5z(45 + 14z + z2) = 0 Factor a trinomial. -5z((9 + z)(5 + 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 '(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 '(5 + z)' equal to zero and attempt to solve: Simplifying 5 + z = 0 Solving 5 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + z = 0 + -5 z = 0 + -5 Combine like terms: 0 + -5 = -5 z = -5 Simplifying z = -5Solution
z = {0, -9, -5}
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