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Simplifying 3z3 + 12z2 = 135z Reorder the terms: 12z2 + 3z3 = 135z Solving 12z2 + 3z3 = 135z Solving for variable 'z'. Reorder the terms: -135z + 12z2 + 3z3 = 135z + -135z Combine like terms: 135z + -135z = 0 -135z + 12z2 + 3z3 = 0 Factor out the Greatest Common Factor (GCF), '3z'. 3z(-45 + 4z + z2) = 0 Factor a trinomial. 3z((-9 + -1z)(5 + -1z)) = 0 Ignore the factor 3.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 + -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 = -9Subproblem 3
Set the factor '(5 + -1z)' equal to zero and attempt to solve: Simplifying 5 + -1z = 0 Solving 5 + -1z = 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 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5Solution
z = {0, -9, 5}
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