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Simplifying 4n3 + -4n2 + 32n = 0 Reorder the terms: 32n + -4n2 + 4n3 = 0 Solving 32n + -4n2 + 4n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4n'. 4n(8 + -1n + n2) = 0 Ignore the factor 4.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 '(8 + -1n + n2)' equal to zero and attempt to solve: Simplifying 8 + -1n + n2 = 0 Solving 8 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -1n + -8 + n2 = 0 + -8 Reorder the terms: 8 + -8 + -1n + n2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n + n2 = 0 + -8 -1n + n2 = 0 + -8 Combine like terms: 0 + -8 = -8 -1n + n2 = -8 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = -8 + 0.25 Reorder the terms: 0.25 + -1n + n2 = -8 + 0.25 Combine like terms: -8 + 0.25 = -7.75 0.25 + -1n + n2 = -7.75 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = -7.75 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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