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Simplifying (3n + -4)(n + 2) = 0 Reorder the terms: (-4 + 3n)(n + 2) = 0 Reorder the terms: (-4 + 3n)(2 + n) = 0 Multiply (-4 + 3n) * (2 + n) (-4(2 + n) + 3n * (2 + n)) = 0 ((2 * -4 + n * -4) + 3n * (2 + n)) = 0 ((-8 + -4n) + 3n * (2 + n)) = 0 (-8 + -4n + (2 * 3n + n * 3n)) = 0 (-8 + -4n + (6n + 3n2)) = 0 Combine like terms: -4n + 6n = 2n (-8 + 2n + 3n2) = 0 Solving -8 + 2n + 3n2 = 0 Solving for variable 'n'. Factor a trinomial. (-2 + -1n)(4 + -3n) = 0Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 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 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2Subproblem 2
Set the factor '(4 + -3n)' equal to zero and attempt to solve: Simplifying 4 + -3n = 0 Solving 4 + -3n = 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 + -3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3n = 0 + -4 -3n = 0 + -4 Combine like terms: 0 + -4 = -4 -3n = -4 Divide each side by '-3'. n = 1.333333333 Simplifying n = 1.333333333Solution
n = {-2, 1.333333333}
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