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Simplifying (4n + -1)(3n + 4) = 0 Reorder the terms: (-1 + 4n)(3n + 4) = 0 Reorder the terms: (-1 + 4n)(4 + 3n) = 0 Multiply (-1 + 4n) * (4 + 3n) (-1(4 + 3n) + 4n * (4 + 3n)) = 0 ((4 * -1 + 3n * -1) + 4n * (4 + 3n)) = 0 ((-4 + -3n) + 4n * (4 + 3n)) = 0 (-4 + -3n + (4 * 4n + 3n * 4n)) = 0 (-4 + -3n + (16n + 12n2)) = 0 Combine like terms: -3n + 16n = 13n (-4 + 13n + 12n2) = 0 Solving -4 + 13n + 12n2 = 0 Solving for variable 'n'. Factor a trinomial. (-4 + -3n)(1 + -4n) = 0Subproblem 1
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 = -1.333333333Subproblem 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 = 0.25Solution
n = {-1.333333333, 0.25}
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