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Simplifying 5(3z + -6) + 15(2 + -1z3) = 0 Reorder the terms: 5(-6 + 3z) + 15(2 + -1z3) = 0 (-6 * 5 + 3z * 5) + 15(2 + -1z3) = 0 (-30 + 15z) + 15(2 + -1z3) = 0 -30 + 15z + (2 * 15 + -1z3 * 15) = 0 -30 + 15z + (30 + -15z3) = 0 Reorder the terms: -30 + 30 + 15z + -15z3 = 0 Combine like terms: -30 + 30 = 0 0 + 15z + -15z3 = 0 15z + -15z3 = 0 Solving 15z + -15z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '15z'. 15z(1 + -1z2) = 0 Factor a difference between two squares. 15z((1 + z)(1 + -1z)) = 0 Ignore the factor 15.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 '(1 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Subproblem 3
Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Solution
z = {0, -1, 1}
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