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Simplifying 3(z + 5)(-1z + 8) = 0 Reorder the terms: 3(5 + z)(-1z + 8) = 0 Reorder the terms: 3(5 + z)(8 + -1z) = 0 Multiply (5 + z) * (8 + -1z) 3(5(8 + -1z) + z(8 + -1z)) = 0 3((8 * 5 + -1z * 5) + z(8 + -1z)) = 0 3((40 + -5z) + z(8 + -1z)) = 0 3(40 + -5z + (8 * z + -1z * z)) = 0 3(40 + -5z + (8z + -1z2)) = 0 Combine like terms: -5z + 8z = 3z 3(40 + 3z + -1z2) = 0 (40 * 3 + 3z * 3 + -1z2 * 3) = 0 (120 + 9z + -3z2) = 0 Solving 120 + 9z + -3z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3'. 3(40 + 3z + -1z2) = 0 Factor a trinomial. 3((8 + -1z)(5 + z)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + -1z)' equal to zero and attempt to solve: Simplifying 8 + -1z = 0 Solving 8 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1z = 0 + -8 -1z = 0 + -8 Combine like terms: 0 + -8 = -8 -1z = -8 Divide each side by '-1'. z = 8 Simplifying z = 8Subproblem 2
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 = {8, -5}
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