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Simplifying (4n + -5)(n + -4) = 0 Reorder the terms: (-5 + 4n)(n + -4) = 0 Reorder the terms: (-5 + 4n)(-4 + n) = 0 Multiply (-5 + 4n) * (-4 + n) (-5(-4 + n) + 4n * (-4 + n)) = 0 ((-4 * -5 + n * -5) + 4n * (-4 + n)) = 0 ((20 + -5n) + 4n * (-4 + n)) = 0 (20 + -5n + (-4 * 4n + n * 4n)) = 0 (20 + -5n + (-16n + 4n2)) = 0 Combine like terms: -5n + -16n = -21n (20 + -21n + 4n2) = 0 Solving 20 + -21n + 4n2 = 0 Solving for variable 'n'. Factor a trinomial. (5 + -4n)(4 + -1n) = 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 '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Solution
n = {1.25, 4}
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