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Simplifying (2n + 3)(n + 6) = 0 Reorder the terms: (3 + 2n)(n + 6) = 0 Reorder the terms: (3 + 2n)(6 + n) = 0 Multiply (3 + 2n) * (6 + n) (3(6 + n) + 2n * (6 + n)) = 0 ((6 * 3 + n * 3) + 2n * (6 + n)) = 0 ((18 + 3n) + 2n * (6 + n)) = 0 (18 + 3n + (6 * 2n + n * 2n)) = 0 (18 + 3n + (12n + 2n2)) = 0 Combine like terms: 3n + 12n = 15n (18 + 15n + 2n2) = 0 Solving 18 + 15n + 2n2 = 0 Solving for variable 'n'. Factor a trinomial. (6 + n)(3 + 2n) = 0Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve: Simplifying 6 + n = 0 Solving 6 + n = 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 + n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + n = 0 + -6 n = 0 + -6 Combine like terms: 0 + -6 = -6 n = -6 Simplifying n = -6Subproblem 2
Set the factor '(3 + 2n)' equal to zero and attempt to solve: Simplifying 3 + 2n = 0 Solving 3 + 2n = 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 + 2n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2n = 0 + -3 2n = 0 + -3 Combine like terms: 0 + -3 = -3 2n = -3 Divide each side by '2'. n = -1.5 Simplifying n = -1.5Solution
n = {-6, -1.5}
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