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Simplifying 4z3 = 4z2 + 24z Reorder the terms: 4z3 = 24z + 4z2 Solving 4z3 = 24z + 4z2 Solving for variable 'z'. Reorder the terms: -24z + -4z2 + 4z3 = 24z + 4z2 + -24z + -4z2 Reorder the terms: -24z + -4z2 + 4z3 = 24z + -24z + 4z2 + -4z2 Combine like terms: 24z + -24z = 0 -24z + -4z2 + 4z3 = 0 + 4z2 + -4z2 -24z + -4z2 + 4z3 = 4z2 + -4z2 Combine like terms: 4z2 + -4z2 = 0 -24z + -4z2 + 4z3 = 0 Factor out the Greatest Common Factor (GCF), '4z'. 4z(-6 + -1z + z2) = 0 Factor a trinomial. 4z((-2 + -1z)(3 + -1z)) = 0 Ignore the factor 4.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 '(-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 '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 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 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Solution
z = {0, -2, 3}
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