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Simplifying 12z3 = 14z2 + 48z Reorder the terms: 12z3 = 48z + 14z2 Solving 12z3 = 48z + 14z2 Solving for variable 'z'. Reorder the terms: -48z + -14z2 + 12z3 = 48z + 14z2 + -48z + -14z2 Reorder the terms: -48z + -14z2 + 12z3 = 48z + -48z + 14z2 + -14z2 Combine like terms: 48z + -48z = 0 -48z + -14z2 + 12z3 = 0 + 14z2 + -14z2 -48z + -14z2 + 12z3 = 14z2 + -14z2 Combine like terms: 14z2 + -14z2 = 0 -48z + -14z2 + 12z3 = 0 Factor out the Greatest Common Factor (GCF), '2z'. 2z(-24 + -7z + 6z2) = 0 Factor a trinomial. 2z((-3 + -2z)(8 + -3z)) = 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 '(-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 '(8 + -3z)' equal to zero and attempt to solve: Simplifying 8 + -3z = 0 Solving 8 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3z = 0 + -8 -3z = 0 + -8 Combine like terms: 0 + -8 = -8 -3z = -8 Divide each side by '-3'. z = 2.666666667 Simplifying z = 2.666666667Solution
z = {0, -1.5, 2.666666667}
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