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Simplifying 2n2 + 41 = 19n + 6 Reorder the terms: 41 + 2n2 = 19n + 6 Reorder the terms: 41 + 2n2 = 6 + 19n Solving 41 + 2n2 = 6 + 19n Solving for variable 'n'. Reorder the terms: 41 + -6 + -19n + 2n2 = 6 + 19n + -6 + -19n Combine like terms: 41 + -6 = 35 35 + -19n + 2n2 = 6 + 19n + -6 + -19n Reorder the terms: 35 + -19n + 2n2 = 6 + -6 + 19n + -19n Combine like terms: 6 + -6 = 0 35 + -19n + 2n2 = 0 + 19n + -19n 35 + -19n + 2n2 = 19n + -19n Combine like terms: 19n + -19n = 0 35 + -19n + 2n2 = 0 Factor a trinomial. (5 + -2n)(7 + -1n) = 0Subproblem 1
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 = 2.5Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 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 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {2.5, 7}
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