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