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Simplifying 5z3 + 25z2 = 120z Reorder the terms: 25z2 + 5z3 = 120z Solving 25z2 + 5z3 = 120z Solving for variable 'z'. Reorder the terms: -120z + 25z2 + 5z3 = 120z + -120z Combine like terms: 120z + -120z = 0 -120z + 25z2 + 5z3 = 0 Factor out the Greatest Common Factor (GCF), '5z'. 5z(-24 + 5z + z2) = 0 Factor a trinomial. 5z((-8 + -1z)(3 + -1z)) = 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 '(-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 3
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 = 3Solution
z = {0, -8, 3}
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