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Simplifying 24n3 + -40n2 + 72n = 0 Reorder the terms: 72n + -40n2 + 24n3 = 0 Solving 72n + -40n2 + 24n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '8n'. 8n(9 + -5n + 3n2) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(9 + -5n + 3n2)' equal to zero and attempt to solve: Simplifying 9 + -5n + 3n2 = 0 Solving 9 + -5n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3 + -1.666666667n + n2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -1.666666667n + -3 + n2 = 0 + -3 Reorder the terms: 3 + -3 + -1.666666667n + n2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1.666666667n + n2 = 0 + -3 -1.666666667n + n2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1.666666667n + n2 = -3 The n term is -1.666666667n. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667n + 0.6944444447 + n2 = -3 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667n + n2 = -3 + 0.6944444447 Combine like terms: -3 + 0.6944444447 = -2.3055555553 0.6944444447 + -1.666666667n + n2 = -2.3055555553 Factor a perfect square on the left side: (n + -0.8333333335)(n + -0.8333333335) = -2.3055555553 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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