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Simplifying (n + 7)(n + -4) = 0 Reorder the terms: (7 + n)(n + -4) = 0 Reorder the terms: (7 + n)(-4 + n) = 0 Multiply (7 + n) * (-4 + n) (7(-4 + n) + n(-4 + n)) = 0 ((-4 * 7 + n * 7) + n(-4 + n)) = 0 ((-28 + 7n) + n(-4 + n)) = 0 (-28 + 7n + (-4 * n + n * n)) = 0 (-28 + 7n + (-4n + n2)) = 0 Combine like terms: 7n + -4n = 3n (-28 + 3n + n2) = 0 Solving -28 + 3n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (-7 + -1n)(4 + -1n) = 0Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve: Simplifying -7 + -1n = 0 Solving -7 + -1n = 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 + -1n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1n = 0 + 7 -1n = 0 + 7 Combine like terms: 0 + 7 = 7 -1n = 7 Divide each side by '-1'. n = -7 Simplifying n = -7Subproblem 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 = {-7, 4}
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