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Simplifying 15z3 + -4z2 = 35z Reorder the terms: -4z2 + 15z3 = 35z Solving -4z2 + 15z3 = 35z Solving for variable 'z'. Reorder the terms: -35z + -4z2 + 15z3 = 35z + -35z Combine like terms: 35z + -35z = 0 -35z + -4z2 + 15z3 = 0 Factor out the Greatest Common Factor (GCF), 'z'. z(-35 + -4z + 15z2) = 0 Factor a trinomial. z((-7 + -5z)(5 + -3z)) = 0Subproblem 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 '(-7 + -5z)' equal to zero and attempt to solve: Simplifying -7 + -5z = 0 Solving -7 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -5z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5z = 0 + 7 -5z = 0 + 7 Combine like terms: 0 + 7 = 7 -5z = 7 Divide each side by '-5'. z = -1.4 Simplifying z = -1.4Subproblem 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, -1.4, 1.666666667}
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