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Simplifying (3n + -5)(4n + 5) = 0 Reorder the terms: (-5 + 3n)(4n + 5) = 0 Reorder the terms: (-5 + 3n)(5 + 4n) = 0 Multiply (-5 + 3n) * (5 + 4n) (-5(5 + 4n) + 3n * (5 + 4n)) = 0 ((5 * -5 + 4n * -5) + 3n * (5 + 4n)) = 0 ((-25 + -20n) + 3n * (5 + 4n)) = 0 (-25 + -20n + (5 * 3n + 4n * 3n)) = 0 (-25 + -20n + (15n + 12n2)) = 0 Combine like terms: -20n + 15n = -5n (-25 + -5n + 12n2) = 0 Solving -25 + -5n + 12n2 = 0 Solving for variable 'n'. Factor a trinomial. (-5 + -4n)(5 + -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 '(5 + -3n)' equal to zero and attempt to solve: Simplifying 5 + -3n = 0 Solving 5 + -3n = 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 + -3n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3n = 0 + -5 -3n = 0 + -5 Combine like terms: 0 + -5 = -5 -3n = -5 Divide each side by '-3'. n = 1.666666667 Simplifying n = 1.666666667Solution
n = {-1.25, 1.666666667}
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