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Simplifying (2n + -1)(3n + -4) = 0 Reorder the terms: (-1 + 2n)(3n + -4) = 0 Reorder the terms: (-1 + 2n)(-4 + 3n) = 0 Multiply (-1 + 2n) * (-4 + 3n) (-1(-4 + 3n) + 2n * (-4 + 3n)) = 0 ((-4 * -1 + 3n * -1) + 2n * (-4 + 3n)) = 0 ((4 + -3n) + 2n * (-4 + 3n)) = 0 (4 + -3n + (-4 * 2n + 3n * 2n)) = 0 (4 + -3n + (-8n + 6n2)) = 0 Combine like terms: -3n + -8n = -11n (4 + -11n + 6n2) = 0 Solving 4 + -11n + 6n2 = 0 Solving for variable 'n'. Factor a trinomial. (1 + -2n)(4 + -3n) = 0Subproblem 1
Set the factor '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 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 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5Subproblem 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 = {0.5, 1.333333333}
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