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Simplifying 2n2 + 5n + 4n + 10 = 5(n + 2) + 2(n + 2) Reorder the terms: 10 + 5n + 4n + 2n2 = 5(n + 2) + 2(n + 2) Combine like terms: 5n + 4n = 9n 10 + 9n + 2n2 = 5(n + 2) + 2(n + 2) Reorder the terms: 10 + 9n + 2n2 = 5(2 + n) + 2(n + 2) 10 + 9n + 2n2 = (2 * 5 + n * 5) + 2(n + 2) 10 + 9n + 2n2 = (10 + 5n) + 2(n + 2) Reorder the terms: 10 + 9n + 2n2 = 10 + 5n + 2(2 + n) 10 + 9n + 2n2 = 10 + 5n + (2 * 2 + n * 2) 10 + 9n + 2n2 = 10 + 5n + (4 + 2n) Reorder the terms: 10 + 9n + 2n2 = 10 + 4 + 5n + 2n Combine like terms: 10 + 4 = 14 10 + 9n + 2n2 = 14 + 5n + 2n Combine like terms: 5n + 2n = 7n 10 + 9n + 2n2 = 14 + 7n Solving 10 + 9n + 2n2 = 14 + 7n Solving for variable 'n'. Reorder the terms: 10 + -14 + 9n + -7n + 2n2 = 14 + 7n + -14 + -7n Combine like terms: 10 + -14 = -4 -4 + 9n + -7n + 2n2 = 14 + 7n + -14 + -7n Combine like terms: 9n + -7n = 2n -4 + 2n + 2n2 = 14 + 7n + -14 + -7n Reorder the terms: -4 + 2n + 2n2 = 14 + -14 + 7n + -7n Combine like terms: 14 + -14 = 0 -4 + 2n + 2n2 = 0 + 7n + -7n -4 + 2n + 2n2 = 7n + -7n Combine like terms: 7n + -7n = 0 -4 + 2n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + n + n2) = 0 Factor a trinomial. 2((-2 + -1n)(1 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Solution
n = {-2, 1}
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