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Simplifying 18z3 = 50z Solving 18z3 = 50z Solving for variable 'z'. Reorder the terms: -50z + 18z3 = 50z + -50z Combine like terms: 50z + -50z = 0 -50z + 18z3 = 0 Factor out the Greatest Common Factor (GCF), '2z'. 2z(-25 + 9z2) = 0 Factor a difference between two squares. 2z((5 + 3z)(-5 + 3z)) = 0 Ignore the factor 2.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 '(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 = -1.666666667Subproblem 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, -1.666666667, 1.666666667}
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