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Simplifying 2n(n + 3) + -5(n + 3) = 0 Reorder the terms: 2n(3 + n) + -5(n + 3) = 0 (3 * 2n + n * 2n) + -5(n + 3) = 0 (6n + 2n2) + -5(n + 3) = 0 Reorder the terms: 6n + 2n2 + -5(3 + n) = 0 6n + 2n2 + (3 * -5 + n * -5) = 0 6n + 2n2 + (-15 + -5n) = 0 Reorder the terms: -15 + 6n + -5n + 2n2 = 0 Combine like terms: 6n + -5n = 1n -15 + 1n + 2n2 = 0 Solving -15 + 1n + 2n2 = 0 Solving for variable 'n'. Factor a trinomial. (-3 + -1n)(5 + -2n) = 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 '(5 + -2n)' equal to zero and attempt to solve: Simplifying 5 + -2n = 0 Solving 5 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2n = 0 + -5 -2n = 0 + -5 Combine like terms: 0 + -5 = -5 -2n = -5 Divide each side by '-2'. n = 2.5 Simplifying n = 2.5Solution
n = {-3, 2.5}
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