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Simplifying 9n3 + 12n2 + 32n = 0 Reorder the terms: 32n + 12n2 + 9n3 = 0 Solving 32n + 12n2 + 9n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(32 + 12n + 9n2) = 0Subproblem 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 '(32 + 12n + 9n2)' equal to zero and attempt to solve: Simplifying 32 + 12n + 9n2 = 0 Solving 32 + 12n + 9n2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 3.555555556 + 1.333333333n + n2 = 0 Move the constant term to the right: Add '-3.555555556' to each side of the equation. 3.555555556 + 1.333333333n + -3.555555556 + n2 = 0 + -3.555555556 Reorder the terms: 3.555555556 + -3.555555556 + 1.333333333n + n2 = 0 + -3.555555556 Combine like terms: 3.555555556 + -3.555555556 = 0.000000000 0.000000000 + 1.333333333n + n2 = 0 + -3.555555556 1.333333333n + n2 = 0 + -3.555555556 Combine like terms: 0 + -3.555555556 = -3.555555556 1.333333333n + n2 = -3.555555556 The n term is 1.333333333n. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333n + 0.4444444442 + n2 = -3.555555556 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333n + n2 = -3.555555556 + 0.4444444442 Combine like terms: -3.555555556 + 0.4444444442 = -3.1111111118 0.4444444442 + 1.333333333n + n2 = -3.1111111118 Factor a perfect square on the left side: (n + 0.6666666665)(n + 0.6666666665) = -3.1111111118 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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