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Simplifying 20z3 + -19z2 + 3z = 0 Reorder the terms: 3z + -19z2 + 20z3 = 0 Solving 3z + -19z2 + 20z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(3 + -19z + 20z2) = 0 Factor a trinomial. z((1 + -5z)(3 + -4z)) = 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 + -5z)' equal to zero and attempt to solve: Simplifying 1 + -5z = 0 Solving 1 + -5z = 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 + -5z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5z = 0 + -1 -5z = 0 + -1 Combine like terms: 0 + -1 = -1 -5z = -1 Divide each side by '-5'. z = 0.2 Simplifying z = 0.2Subproblem 3
Set the factor '(3 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Divide each side by '-4'. z = 0.75 Simplifying z = 0.75Solution
z = {0, 0.2, 0.75}
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