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Simplifying 4z3 + 3z2 + -10z = 0 Reorder the terms: -10z + 3z2 + 4z3 = 0 Solving -10z + 3z2 + 4z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-10 + 3z + 4z2) = 0 Factor a trinomial. z((-2 + -1z)(5 + -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 '(-2 + -1z)' equal to zero and attempt to solve: Simplifying -2 + -1z = 0 Solving -2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1z = 0 + 2 -1z = 0 + 2 Combine like terms: 0 + 2 = 2 -1z = 2 Divide each side by '-1'. z = -2 Simplifying z = -2Subproblem 3
Set the factor '(5 + -4z)' equal to zero and attempt to solve: Simplifying 5 + -4z = 0 Solving 5 + -4z = 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 + -4z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4z = 0 + -5 -4z = 0 + -5 Combine like terms: 0 + -5 = -5 -4z = -5 Divide each side by '-4'. z = 1.25 Simplifying z = 1.25Solution
z = {0, -2, 1.25}
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