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Simplifying -5z(z + -6)(z + 9) = 0 Reorder the terms: -5z(-6 + z)(z + 9) = 0 Reorder the terms: -5z(-6 + z)(9 + z) = 0 Multiply (-6 + z) * (9 + z) -5z(-6(9 + z) + z(9 + z)) = 0 -5z((9 * -6 + z * -6) + z(9 + z)) = 0 -5z((-54 + -6z) + z(9 + z)) = 0 -5z(-54 + -6z + (9 * z + z * z)) = 0 -5z(-54 + -6z + (9z + z2)) = 0 Combine like terms: -6z + 9z = 3z -5z(-54 + 3z + z2) = 0 (-54 * -5z + 3z * -5z + z2 * -5z) = 0 (270z + -15z2 + -5z3) = 0 Solving 270z + -15z2 + -5z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z'. 5z(54 + -3z + -1z2) = 0 Factor a trinomial. 5z((6 + -1z)(9 + 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 '(6 + -1z)' equal to zero and attempt to solve: Simplifying 6 + -1z = 0 Solving 6 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1z = 0 + -6 -1z = 0 + -6 Combine like terms: 0 + -6 = -6 -1z = -6 Divide each side by '-1'. z = 6 Simplifying z = 6Subproblem 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, 6, -9}
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