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Simplifying 2z3 + -42z2 + -200z = 0 Reorder the terms: -200z + -42z2 + 2z3 = 0 Solving -200z + -42z2 + 2z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z'. 2z(-100 + -21z + z2) = 0 Factor a trinomial. 2z((-4 + -1z)(25 + -1z)) = 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 '(-4 + -1z)' equal to zero and attempt to solve: Simplifying -4 + -1z = 0 Solving -4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1z = 0 + 4 -1z = 0 + 4 Combine like terms: 0 + 4 = 4 -1z = 4 Divide each side by '-1'. z = -4 Simplifying z = -4Subproblem 3
Set the factor '(25 + -1z)' equal to zero and attempt to solve: Simplifying 25 + -1z = 0 Solving 25 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -1z = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1z = 0 + -25 -1z = 0 + -25 Combine like terms: 0 + -25 = -25 -1z = -25 Divide each side by '-1'. z = 25 Simplifying z = 25Solution
z = {0, -4, 25}
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