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Simplifying 5n2 + 12n + 2 = 3n2 + 7n Reorder the terms: 2 + 12n + 5n2 = 3n2 + 7n Reorder the terms: 2 + 12n + 5n2 = 7n + 3n2 Solving 2 + 12n + 5n2 = 7n + 3n2 Solving for variable 'n'. Reorder the terms: 2 + 12n + -7n + 5n2 + -3n2 = 7n + 3n2 + -7n + -3n2 Combine like terms: 12n + -7n = 5n 2 + 5n + 5n2 + -3n2 = 7n + 3n2 + -7n + -3n2 Combine like terms: 5n2 + -3n2 = 2n2 2 + 5n + 2n2 = 7n + 3n2 + -7n + -3n2 Reorder the terms: 2 + 5n + 2n2 = 7n + -7n + 3n2 + -3n2 Combine like terms: 7n + -7n = 0 2 + 5n + 2n2 = 0 + 3n2 + -3n2 2 + 5n + 2n2 = 3n2 + -3n2 Combine like terms: 3n2 + -3n2 = 0 2 + 5n + 2n2 = 0 Factor a trinomial. (2 + n)(1 + 2n) = 0Subproblem 1
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 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 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Subproblem 2
Set the factor '(1 + 2n)' equal to zero and attempt to solve: Simplifying 1 + 2n = 0 Solving 1 + 2n = 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 + 2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2n = 0 + -1 2n = 0 + -1 Combine like terms: 0 + -1 = -1 2n = -1 Divide each side by '2'. n = -0.5 Simplifying n = -0.5Solution
n = {-2, -0.5}
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