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Simplifying (4n + 5)(3n + -1) = 0 Reorder the terms: (5 + 4n)(3n + -1) = 0 Reorder the terms: (5 + 4n)(-1 + 3n) = 0 Multiply (5 + 4n) * (-1 + 3n) (5(-1 + 3n) + 4n * (-1 + 3n)) = 0 ((-1 * 5 + 3n * 5) + 4n * (-1 + 3n)) = 0 ((-5 + 15n) + 4n * (-1 + 3n)) = 0 (-5 + 15n + (-1 * 4n + 3n * 4n)) = 0 (-5 + 15n + (-4n + 12n2)) = 0 Combine like terms: 15n + -4n = 11n (-5 + 11n + 12n2) = 0 Solving -5 + 11n + 12n2 = 0 Solving for variable 'n'. Factor a trinomial. (-5 + -4n)(1 + -3n) = 0Subproblem 1
Set the factor '(-5 + -4n)' equal to zero and attempt to solve: Simplifying -5 + -4n = 0 Solving -5 + -4n = 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 + -4n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4n = 0 + 5 -4n = 0 + 5 Combine like terms: 0 + 5 = 5 -4n = 5 Divide each side by '-4'. n = -1.25 Simplifying n = -1.25Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve: Simplifying 1 + -3n = 0 Solving 1 + -3n = 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 + -3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3n = 0 + -1 -3n = 0 + -1 Combine like terms: 0 + -1 = -1 -3n = -1 Divide each side by '-3'. n = 0.3333333333 Simplifying n = 0.3333333333Solution
n = {-1.25, 0.3333333333}
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