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Simplifying (3n2 + 13n3 + 5n) + -1(7n + 4n3) = 0 Reorder the terms: (5n + 3n2 + 13n3) + -1(7n + 4n3) = 0 Remove parenthesis around (5n + 3n2 + 13n3) 5n + 3n2 + 13n3 + -1(7n + 4n3) = 0 5n + 3n2 + 13n3 + (7n * -1 + 4n3 * -1) = 0 5n + 3n2 + 13n3 + (-7n + -4n3) = 0 Reorder the terms: 5n + -7n + 3n2 + 13n3 + -4n3 = 0 Combine like terms: 5n + -7n = -2n -2n + 3n2 + 13n3 + -4n3 = 0 Combine like terms: 13n3 + -4n3 = 9n3 -2n + 3n2 + 9n3 = 0 Solving -2n + 3n2 + 9n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(-2 + 3n + 9n2) = 0 Factor a trinomial. n((-2 + -3n)(1 + -3n)) = 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 '(-2 + -3n)' equal to zero and attempt to solve: Simplifying -2 + -3n = 0 Solving -2 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3n = 0 + 2 -3n = 0 + 2 Combine like terms: 0 + 2 = 2 -3n = 2 Divide each side by '-3'. n = -0.6666666667 Simplifying n = -0.6666666667Subproblem 3
Set the factor '(1 + -3n)' equal to zero and attempt to solve: Simplifying 1 + -3n = 0 Solving 1 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3n = 0 + -1 -3n = 0 + -1 Combine like terms: 0 + -1 = -1 -3n = -1 Divide each side by '-3'. n = 0.3333333333 Simplifying n = 0.3333333333Solution
n = {0, -0.6666666667, 0.3333333333}
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