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Simplifying (4n + -5)(3n + -2) = 0 Reorder the terms: (-5 + 4n)(3n + -2) = 0 Reorder the terms: (-5 + 4n)(-2 + 3n) = 0 Multiply (-5 + 4n) * (-2 + 3n) (-5(-2 + 3n) + 4n * (-2 + 3n)) = 0 ((-2 * -5 + 3n * -5) + 4n * (-2 + 3n)) = 0 ((10 + -15n) + 4n * (-2 + 3n)) = 0 (10 + -15n + (-2 * 4n + 3n * 4n)) = 0 (10 + -15n + (-8n + 12n2)) = 0 Combine like terms: -15n + -8n = -23n (10 + -23n + 12n2) = 0 Solving 10 + -23n + 12n2 = 0 Solving for variable 'n'. Factor a trinomial. (2 + -3n)(5 + -4n) = 0Subproblem 1
Set the factor '(2 + -3n)' equal to zero and attempt to solve: Simplifying 2 + -3n = 0 Solving 2 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3n = 0 + -2 -3n = 0 + -2 Combine like terms: 0 + -2 = -2 -3n = -2 Divide each side by '-3'. n = 0.6666666667 Simplifying n = 0.6666666667Subproblem 2
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 = 1.25Solution
n = {0.6666666667, 1.25}
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