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Simplifying (n + 3)(n + -2) = 36 Reorder the terms: (3 + n)(n + -2) = 36 Reorder the terms: (3 + n)(-2 + n) = 36 Multiply (3 + n) * (-2 + n) (3(-2 + n) + n(-2 + n)) = 36 ((-2 * 3 + n * 3) + n(-2 + n)) = 36 ((-6 + 3n) + n(-2 + n)) = 36 (-6 + 3n + (-2 * n + n * n)) = 36 (-6 + 3n + (-2n + n2)) = 36 Combine like terms: 3n + -2n = 1n (-6 + 1n + n2) = 36 Solving -6 + 1n + n2 = 36 Solving for variable 'n'. Reorder the terms: -6 + -36 + 1n + n2 = 36 + -36 Combine like terms: -6 + -36 = -42 -42 + 1n + n2 = 36 + -36 Combine like terms: 36 + -36 = 0 -42 + 1n + n2 = 0 Factor a trinomial. (-7 + -1n)(6 + -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 '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6Solution
n = {-7, 6}
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