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Simplifying n(4n + 1)(5n + -2) = 0 Reorder the terms: n(1 + 4n)(5n + -2) = 0 Reorder the terms: n(1 + 4n)(-2 + 5n) = 0 Multiply (1 + 4n) * (-2 + 5n) n(1(-2 + 5n) + 4n * (-2 + 5n)) = 0 n((-2 * 1 + 5n * 1) + 4n * (-2 + 5n)) = 0 n((-2 + 5n) + 4n * (-2 + 5n)) = 0 n(-2 + 5n + (-2 * 4n + 5n * 4n)) = 0 n(-2 + 5n + (-8n + 20n2)) = 0 Combine like terms: 5n + -8n = -3n n(-2 + -3n + 20n2) = 0 (-2 * n + -3n * n + 20n2 * n) = 0 (-2n + -3n2 + 20n3) = 0 Solving -2n + -3n2 + 20n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(-2 + -3n + 20n2) = 0 Factor a trinomial. n((-1 + -4n)(2 + -5n)) = 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 '(-1 + -4n)' equal to zero and attempt to solve: Simplifying -1 + -4n = 0 Solving -1 + -4n = 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 + -4n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4n = 0 + 1 -4n = 0 + 1 Combine like terms: 0 + 1 = 1 -4n = 1 Divide each side by '-4'. n = -0.25 Simplifying n = -0.25Subproblem 3
Set the factor '(2 + -5n)' equal to zero and attempt to solve: Simplifying 2 + -5n = 0 Solving 2 + -5n = 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 + -5n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5n = 0 + -2 -5n = 0 + -2 Combine like terms: 0 + -2 = -2 -5n = -2 Divide each side by '-5'. n = 0.4 Simplifying n = 0.4Solution
n = {0, -0.25, 0.4}
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