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Simplifying 2n2 = 14 + 3n Solving 2n2 = 14 + 3n Solving for variable 'n'. Reorder the terms: -14 + -3n + 2n2 = 14 + 3n + -14 + -3n Reorder the terms: -14 + -3n + 2n2 = 14 + -14 + 3n + -3n Combine like terms: 14 + -14 = 0 -14 + -3n + 2n2 = 0 + 3n + -3n -14 + -3n + 2n2 = 3n + -3n Combine like terms: 3n + -3n = 0 -14 + -3n + 2n2 = 0 Factor a trinomial. (-2 + -1n)(7 + -2n) = 0Subproblem 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 '(7 + -2n)' equal to zero and attempt to solve: Simplifying 7 + -2n = 0 Solving 7 + -2n = 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 + -2n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2n = 0 + -7 -2n = 0 + -7 Combine like terms: 0 + -7 = -7 -2n = -7 Divide each side by '-2'. n = 3.5 Simplifying n = 3.5Solution
n = {-2, 3.5}
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