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Simplifying 5n3 + 15n2 + 25n = 0 Reorder the terms: 25n + 15n2 + 5n3 = 0 Solving 25n + 15n2 + 5n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5n'. 5n(5 + 3n + n2) = 0 Ignore the factor 5.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 '(5 + 3n + n2)' equal to zero and attempt to solve: Simplifying 5 + 3n + n2 = 0 Solving 5 + 3n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 3n + -5 + n2 = 0 + -5 Reorder the terms: 5 + -5 + 3n + n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3n + n2 = 0 + -5 3n + n2 = 0 + -5 Combine like terms: 0 + -5 = -5 3n + n2 = -5 The n term is 3n. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3n + 2.25 + n2 = -5 + 2.25 Reorder the terms: 2.25 + 3n + n2 = -5 + 2.25 Combine like terms: -5 + 2.25 = -2.75 2.25 + 3n + n2 = -2.75 Factor a perfect square on the left side: (n + 1.5)(n + 1.5) = -2.75 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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