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Simplifying 30n3 + 18n2 + 54n = 0 Reorder the terms: 54n + 18n2 + 30n3 = 0 Solving 54n + 18n2 + 30n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '6n'. 6n(9 + 3n + 5n2) = 0 Ignore the factor 6.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 + 3n + 5n2)' equal to zero and attempt to solve: Simplifying 9 + 3n + 5n2 = 0 Solving 9 + 3n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + 0.6n + n2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + 0.6n + -1.8 + n2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + 0.6n + n2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + 0.6n + n2 = 0 + -1.8 0.6n + n2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 0.6n + n2 = -1.8 The n term is 0.6n. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6n + 0.09 + n2 = -1.8 + 0.09 Reorder the terms: 0.09 + 0.6n + n2 = -1.8 + 0.09 Combine like terms: -1.8 + 0.09 = -1.71 0.09 + 0.6n + n2 = -1.71 Factor a perfect square on the left side: (n + 0.3)(n + 0.3) = -1.71 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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