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Simplifying (3n + -4)(n + 4) = 0 Reorder the terms: (-4 + 3n)(n + 4) = 0 Reorder the terms: (-4 + 3n)(4 + n) = 0 Multiply (-4 + 3n) * (4 + n) (-4(4 + n) + 3n * (4 + n)) = 0 ((4 * -4 + n * -4) + 3n * (4 + n)) = 0 ((-16 + -4n) + 3n * (4 + n)) = 0 (-16 + -4n + (4 * 3n + n * 3n)) = 0 (-16 + -4n + (12n + 3n2)) = 0 Combine like terms: -4n + 12n = 8n (-16 + 8n + 3n2) = 0 Solving -16 + 8n + 3n2 = 0 Solving for variable 'n'. Factor a trinomial. (-4 + -1n)(4 + -3n) = 0Subproblem 1
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 = -4Subproblem 2
Set the factor '(4 + -3n)' equal to zero and attempt to solve: Simplifying 4 + -3n = 0 Solving 4 + -3n = 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 + -3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3n = 0 + -4 -3n = 0 + -4 Combine like terms: 0 + -4 = -4 -3n = -4 Divide each side by '-3'. n = 1.333333333 Simplifying n = 1.333333333Solution
n = {-4, 1.333333333}
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