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Simplifying 5z3 + 35z2 + -150z = 0 Reorder the terms: -150z + 35z2 + 5z3 = 0 Solving -150z + 35z2 + 5z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z'. 5z(-30 + 7z + z2) = 0 Factor a trinomial. 5z((-10 + -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 '(-10 + -1z)' equal to zero and attempt to solve: Simplifying -10 + -1z = 0 Solving -10 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1z = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1z = 0 + 10 -1z = 0 + 10 Combine like terms: 0 + 10 = 10 -1z = 10 Divide each side by '-1'. z = -10 Simplifying z = -10Subproblem 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, -10, 3}
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