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Simplifying 30z3 = 35z2 + 25z Reorder the terms: 30z3 = 25z + 35z2 Solving 30z3 = 25z + 35z2 Solving for variable 'z'. Reorder the terms: -25z + -35z2 + 30z3 = 25z + 35z2 + -25z + -35z2 Reorder the terms: -25z + -35z2 + 30z3 = 25z + -25z + 35z2 + -35z2 Combine like terms: 25z + -25z = 0 -25z + -35z2 + 30z3 = 0 + 35z2 + -35z2 -25z + -35z2 + 30z3 = 35z2 + -35z2 Combine like terms: 35z2 + -35z2 = 0 -25z + -35z2 + 30z3 = 0 Factor out the Greatest Common Factor (GCF), '5z'. 5z(-5 + -7z + 6z2) = 0 Factor a trinomial. 5z((-1 + -2z)(5 + -3z)) = 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 '(-1 + -2z)' equal to zero and attempt to solve: Simplifying -1 + -2z = 0 Solving -1 + -2z = 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 + -2z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2z = 0 + 1 -2z = 0 + 1 Combine like terms: 0 + 1 = 1 -2z = 1 Divide each side by '-2'. z = -0.5 Simplifying z = -0.5Subproblem 3
Set the factor '(5 + -3z)' equal to zero and attempt to solve: Simplifying 5 + -3z = 0 Solving 5 + -3z = 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 + -3z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3z = 0 + -5 -3z = 0 + -5 Combine like terms: 0 + -5 = -5 -3z = -5 Divide each side by '-3'. z = 1.666666667 Simplifying z = 1.666666667Solution
z = {0, -0.5, 1.666666667}
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