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Simplifying -5(z + -9)(-1z + -3) = 0 Reorder the terms: -5(-9 + z)(-1z + -3) = 0 Reorder the terms: -5(-9 + z)(-3 + -1z) = 0 Multiply (-9 + z) * (-3 + -1z) -5(-9(-3 + -1z) + z(-3 + -1z)) = 0 -5((-3 * -9 + -1z * -9) + z(-3 + -1z)) = 0 -5((27 + 9z) + z(-3 + -1z)) = 0 -5(27 + 9z + (-3 * z + -1z * z)) = 0 -5(27 + 9z + (-3z + -1z2)) = 0 Combine like terms: 9z + -3z = 6z -5(27 + 6z + -1z2) = 0 (27 * -5 + 6z * -5 + -1z2 * -5) = 0 (-135 + -30z + 5z2) = 0 Solving -135 + -30z + 5z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5'. 5(-27 + -6z + z2) = 0 Factor a trinomial. 5((-3 + -1z)(9 + -1z)) = 0 Ignore the factor 5.Subproblem 1
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 = -3Subproblem 2
Set the factor '(9 + -1z)' equal to zero and attempt to solve: Simplifying 9 + -1z = 0 Solving 9 + -1z = 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 + -1z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1z = 0 + -9 -1z = 0 + -9 Combine like terms: 0 + -9 = -9 -1z = -9 Divide each side by '-1'. z = 9 Simplifying z = 9Solution
z = {-3, 9}
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