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Simplifying (4n + -7)(4n + 5) = 0 Reorder the terms: (-7 + 4n)(4n + 5) = 0 Reorder the terms: (-7 + 4n)(5 + 4n) = 0 Multiply (-7 + 4n) * (5 + 4n) (-7(5 + 4n) + 4n * (5 + 4n)) = 0 ((5 * -7 + 4n * -7) + 4n * (5 + 4n)) = 0 ((-35 + -28n) + 4n * (5 + 4n)) = 0 (-35 + -28n + (5 * 4n + 4n * 4n)) = 0 (-35 + -28n + (20n + 16n2)) = 0 Combine like terms: -28n + 20n = -8n (-35 + -8n + 16n2) = 0 Solving -35 + -8n + 16n2 = 0 Solving for variable 'n'. Factor a trinomial. (-5 + -4n)(7 + -4n) = 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 '(7 + -4n)' equal to zero and attempt to solve: Simplifying 7 + -4n = 0 Solving 7 + -4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4n = 0 + -7 -4n = 0 + -7 Combine like terms: 0 + -7 = -7 -4n = -7 Divide each side by '-4'. n = 1.75 Simplifying n = 1.75Solution
n = {-1.25, 1.75}
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