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Simplifying n(2n + -5)(10n + 3) = 0 Reorder the terms: n(-5 + 2n)(10n + 3) = 0 Reorder the terms: n(-5 + 2n)(3 + 10n) = 0 Multiply (-5 + 2n) * (3 + 10n) n(-5(3 + 10n) + 2n * (3 + 10n)) = 0 n((3 * -5 + 10n * -5) + 2n * (3 + 10n)) = 0 n((-15 + -50n) + 2n * (3 + 10n)) = 0 n(-15 + -50n + (3 * 2n + 10n * 2n)) = 0 n(-15 + -50n + (6n + 20n2)) = 0 Combine like terms: -50n + 6n = -44n n(-15 + -44n + 20n2) = 0 (-15 * n + -44n * n + 20n2 * n) = 0 (-15n + -44n2 + 20n3) = 0 Solving -15n + -44n2 + 20n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(-15 + -44n + 20n2) = 0 Factor a trinomial. n((-3 + -10n)(5 + -2n)) = 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 '(-3 + -10n)' equal to zero and attempt to solve: Simplifying -3 + -10n = 0 Solving -3 + -10n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -10n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -10n = 0 + 3 -10n = 0 + 3 Combine like terms: 0 + 3 = 3 -10n = 3 Divide each side by '-10'. n = -0.3 Simplifying n = -0.3Subproblem 3
Set the factor '(5 + -2n)' equal to zero and attempt to solve: Simplifying 5 + -2n = 0 Solving 5 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2n = 0 + -5 -2n = 0 + -5 Combine like terms: 0 + -5 = -5 -2n = -5 Divide each side by '-2'. n = 2.5 Simplifying n = 2.5Solution
n = {0, -0.3, 2.5}
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