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Simplifying (n + -8)(4n + -3) = 0 Reorder the terms: (-8 + n)(4n + -3) = 0 Reorder the terms: (-8 + n)(-3 + 4n) = 0 Multiply (-8 + n) * (-3 + 4n) (-8(-3 + 4n) + n(-3 + 4n)) = 0 ((-3 * -8 + 4n * -8) + n(-3 + 4n)) = 0 ((24 + -32n) + n(-3 + 4n)) = 0 (24 + -32n + (-3 * n + 4n * n)) = 0 (24 + -32n + (-3n + 4n2)) = 0 Combine like terms: -32n + -3n = -35n (24 + -35n + 4n2) = 0 Solving 24 + -35n + 4n2 = 0 Solving for variable 'n'. Factor a trinomial. (3 + -4n)(8 + -1n) = 0Subproblem 1
Set the factor '(3 + -4n)' equal to zero and attempt to solve: Simplifying 3 + -4n = 0 Solving 3 + -4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4n = 0 + -3 -4n = 0 + -3 Combine like terms: 0 + -3 = -3 -4n = -3 Divide each side by '-4'. n = 0.75 Simplifying n = 0.75Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 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 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8Solution
n = {0.75, 8}
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