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Simplifying 5z3 = 4z2 + 9z Reorder the terms: 5z3 = 9z + 4z2 Solving 5z3 = 9z + 4z2 Solving for variable 'z'. Reorder the terms: -9z + -4z2 + 5z3 = 9z + 4z2 + -9z + -4z2 Reorder the terms: -9z + -4z2 + 5z3 = 9z + -9z + 4z2 + -4z2 Combine like terms: 9z + -9z = 0 -9z + -4z2 + 5z3 = 0 + 4z2 + -4z2 -9z + -4z2 + 5z3 = 4z2 + -4z2 Combine like terms: 4z2 + -4z2 = 0 -9z + -4z2 + 5z3 = 0 Factor out the Greatest Common Factor (GCF), 'z'. z(-9 + -4z + 5z2) = 0 Factor a trinomial. z((-1 + -1z)(9 + -5z)) = 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 '(-1 + -1z)' equal to zero and attempt to solve: Simplifying -1 + -1z = 0 Solving -1 + -1z = 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 + -1z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1z = 0 + 1 -1z = 0 + 1 Combine like terms: 0 + 1 = 1 -1z = 1 Divide each side by '-1'. z = -1 Simplifying z = -1Subproblem 3
Set the factor '(9 + -5z)' equal to zero and attempt to solve: Simplifying 9 + -5z = 0 Solving 9 + -5z = 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 + -5z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5z = 0 + -9 -5z = 0 + -9 Combine like terms: 0 + -9 = -9 -5z = -9 Divide each side by '-5'. z = 1.8 Simplifying z = 1.8Solution
z = {0, -1, 1.8}
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