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Simplifying 3n(n2 + -4n + 9) = 0 Reorder the terms: 3n(9 + -4n + n2) = 0 (9 * 3n + -4n * 3n + n2 * 3n) = 0 (27n + -12n2 + 3n3) = 0 Solving 27n + -12n2 + 3n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3n'. 3n(9 + -4n + n2) = 0 Ignore the factor 3.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 + -4n + n2)' equal to zero and attempt to solve: Simplifying 9 + -4n + n2 = 0 Solving 9 + -4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -4n + -9 + n2 = 0 + -9 Reorder the terms: 9 + -9 + -4n + n2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4n + n2 = 0 + -9 -4n + n2 = 0 + -9 Combine like terms: 0 + -9 = -9 -4n + n2 = -9 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = -9 + 4 Reorder the terms: 4 + -4n + n2 = -9 + 4 Combine like terms: -9 + 4 = -5 4 + -4n + n2 = -5 Factor a perfect square on the left side: (n + -2)(n + -2) = -5 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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