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Simplifying 2z3 + 9z2 = 5z Reorder the terms: 9z2 + 2z3 = 5z Solving 9z2 + 2z3 = 5z Solving for variable 'z'. Reorder the terms: -5z + 9z2 + 2z3 = 5z + -5z Combine like terms: 5z + -5z = 0 -5z + 9z2 + 2z3 = 0 Factor out the Greatest Common Factor (GCF), 'z'. z(-5 + 9z + 2z2) = 0 Factor a trinomial. z((-5 + -1z)(1 + -2z)) = 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 '(-5 + -1z)' equal to zero and attempt to solve: Simplifying -5 + -1z = 0 Solving -5 + -1z = 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 + -1z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1z = 0 + 5 -1z = 0 + 5 Combine like terms: 0 + 5 = 5 -1z = 5 Divide each side by '-1'. z = -5 Simplifying z = -5Subproblem 3
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 = 0.5Solution
z = {0, -5, 0.5}
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