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Simplifying (9n + -8)(5n + 6) = 0 Reorder the terms: (-8 + 9n)(5n + 6) = 0 Reorder the terms: (-8 + 9n)(6 + 5n) = 0 Multiply (-8 + 9n) * (6 + 5n) (-8(6 + 5n) + 9n * (6 + 5n)) = 0 ((6 * -8 + 5n * -8) + 9n * (6 + 5n)) = 0 ((-48 + -40n) + 9n * (6 + 5n)) = 0 (-48 + -40n + (6 * 9n + 5n * 9n)) = 0 (-48 + -40n + (54n + 45n2)) = 0 Combine like terms: -40n + 54n = 14n (-48 + 14n + 45n2) = 0 Solving -48 + 14n + 45n2 = 0 Solving for variable 'n'. Factor a trinomial. (-6 + -5n)(8 + -9n) = 0Subproblem 1
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 = -1.2Subproblem 2
Set the factor '(8 + -9n)' equal to zero and attempt to solve: Simplifying 8 + -9n = 0 Solving 8 + -9n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -9n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -9n = 0 + -8 -9n = 0 + -8 Combine like terms: 0 + -8 = -8 -9n = -8 Divide each side by '-9'. n = 0.8888888889 Simplifying n = 0.8888888889Solution
n = {-1.2, 0.8888888889}
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