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Simplifying (5n + -6)(3n + 5) = 0 Reorder the terms: (-6 + 5n)(3n + 5) = 0 Reorder the terms: (-6 + 5n)(5 + 3n) = 0 Multiply (-6 + 5n) * (5 + 3n) (-6(5 + 3n) + 5n * (5 + 3n)) = 0 ((5 * -6 + 3n * -6) + 5n * (5 + 3n)) = 0 ((-30 + -18n) + 5n * (5 + 3n)) = 0 (-30 + -18n + (5 * 5n + 3n * 5n)) = 0 (-30 + -18n + (25n + 15n2)) = 0 Combine like terms: -18n + 25n = 7n (-30 + 7n + 15n2) = 0 Solving -30 + 7n + 15n2 = 0 Solving for variable 'n'. Factor a trinomial. (-5 + -3n)(6 + -5n) = 0Subproblem 1
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 = -1.666666667Subproblem 2
Set the factor '(6 + -5n)' equal to zero and attempt to solve: Simplifying 6 + -5n = 0 Solving 6 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5n = 0 + -6 -5n = 0 + -6 Combine like terms: 0 + -6 = -6 -5n = -6 Divide each side by '-5'. n = 1.2 Simplifying n = 1.2Solution
n = {-1.666666667, 1.2}
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