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Simplifying (4n + -3n3) + -1(3n3 + -4n) = 0 Remove parenthesis around (4n + -3n3) 4n + -3n3 + -1(3n3 + -4n) = 0 Reorder the terms: 4n + -3n3 + -1(-4n + 3n3) = 0 4n + -3n3 + (-4n * -1 + 3n3 * -1) = 0 4n + -3n3 + (4n + -3n3) = 0 Reorder the terms: 4n + 4n + -3n3 + -3n3 = 0 Combine like terms: 4n + 4n = 8n 8n + -3n3 + -3n3 = 0 Combine like terms: -3n3 + -3n3 = -6n3 8n + -6n3 = 0 Solving 8n + -6n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2n'. 2n(4 + -3n2) = 0 Ignore the factor 2.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 '(4 + -3n2)' equal to zero and attempt to solve: Simplifying 4 + -3n2 = 0 Solving 4 + -3n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3n2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3n2 = 0 + -4 -3n2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3n2 = -4 Divide each side by '-3'. n2 = 1.333333333 Simplifying n2 = 1.333333333 Take the square root of each side: n = {-1.154700538, 1.154700538}Solution
n = {0, -1.154700538, 1.154700538}
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