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Simplifying 24z3 = 20z2 + 84z Reorder the terms: 24z3 = 84z + 20z2 Solving 24z3 = 84z + 20z2 Solving for variable 'z'. Reorder the terms: -84z + -20z2 + 24z3 = 84z + 20z2 + -84z + -20z2 Reorder the terms: -84z + -20z2 + 24z3 = 84z + -84z + 20z2 + -20z2 Combine like terms: 84z + -84z = 0 -84z + -20z2 + 24z3 = 0 + 20z2 + -20z2 -84z + -20z2 + 24z3 = 20z2 + -20z2 Combine like terms: 20z2 + -20z2 = 0 -84z + -20z2 + 24z3 = 0 Factor out the Greatest Common Factor (GCF), '4z'. 4z(-21 + -5z + 6z2) = 0 Factor a trinomial. 4z((-3 + -2z)(7 + -3z)) = 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 '(-3 + -2z)' equal to zero and attempt to solve: Simplifying -3 + -2z = 0 Solving -3 + -2z = 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 + -2z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2z = 0 + 3 -2z = 0 + 3 Combine like terms: 0 + 3 = 3 -2z = 3 Divide each side by '-2'. z = -1.5 Simplifying z = -1.5Subproblem 3
Set the factor '(7 + -3z)' equal to zero and attempt to solve: Simplifying 7 + -3z = 0 Solving 7 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3z = 0 + -7 -3z = 0 + -7 Combine like terms: 0 + -7 = -7 -3z = -7 Divide each side by '-3'. z = 2.333333333 Simplifying z = 2.333333333Solution
z = {0, -1.5, 2.333333333}
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