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Simplifying n(3n + -2) = 40 Reorder the terms: n(-2 + 3n) = 40 (-2 * n + 3n * n) = 40 (-2n + 3n2) = 40 Solving -2n + 3n2 = 40 Solving for variable 'n'. Reorder the terms: -40 + -2n + 3n2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + -2n + 3n2 = 0 Factor a trinomial. (-10 + -3n)(4 + -1n) = 0Subproblem 1
Set the factor '(-10 + -3n)' equal to zero and attempt to solve: Simplifying -10 + -3n = 0 Solving -10 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -3n = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3n = 0 + 10 -3n = 0 + 10 Combine like terms: 0 + 10 = 10 -3n = 10 Divide each side by '-3'. n = -3.333333333 Simplifying n = -3.333333333Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 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 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Solution
n = {-3.333333333, 4}
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