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Simplifying 3n + -5n3 + -7n + 7n2 + -4n3 = 0 Reorder the terms: 3n + -7n + 7n2 + -5n3 + -4n3 = 0 Combine like terms: 3n + -7n = -4n -4n + 7n2 + -5n3 + -4n3 = 0 Combine like terms: -5n3 + -4n3 = -9n3 -4n + 7n2 + -9n3 = 0 Solving -4n + 7n2 + -9n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(-4 + 7n + -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 '(-4 + 7n + -9n2)' equal to zero and attempt to solve: Simplifying -4 + 7n + -9n2 = 0 Solving -4 + 7n + -9n2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 0.4444444444 + -0.7777777778n + n2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -0.7777777778n + -0.4444444444 + n2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -0.7777777778n + n2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -0.7777777778n + n2 = 0 + -0.4444444444 -0.7777777778n + n2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -0.7777777778n + n2 = -0.4444444444 The n term is -0.7777777778n. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778n + 0.1512345679 + n2 = -0.4444444444 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778n + n2 = -0.4444444444 + 0.1512345679 Combine like terms: -0.4444444444 + 0.1512345679 = -0.2932098765 0.1512345679 + -0.7777777778n + n2 = -0.2932098765 Factor a perfect square on the left side: (n + -0.3888888889)(n + -0.3888888889) = -0.2932098765 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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