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Simplifying 11n2 + -3 = -5 + 6n2 + 7n Reorder the terms: -3 + 11n2 = -5 + 6n2 + 7n Reorder the terms: -3 + 11n2 = -5 + 7n + 6n2 Solving -3 + 11n2 = -5 + 7n + 6n2 Solving for variable 'n'. Reorder the terms: -3 + 5 + -7n + 11n2 + -6n2 = -5 + 7n + 6n2 + 5 + -7n + -6n2 Combine like terms: -3 + 5 = 2 2 + -7n + 11n2 + -6n2 = -5 + 7n + 6n2 + 5 + -7n + -6n2 Combine like terms: 11n2 + -6n2 = 5n2 2 + -7n + 5n2 = -5 + 7n + 6n2 + 5 + -7n + -6n2 Reorder the terms: 2 + -7n + 5n2 = -5 + 5 + 7n + -7n + 6n2 + -6n2 Combine like terms: -5 + 5 = 0 2 + -7n + 5n2 = 0 + 7n + -7n + 6n2 + -6n2 2 + -7n + 5n2 = 7n + -7n + 6n2 + -6n2 Combine like terms: 7n + -7n = 0 2 + -7n + 5n2 = 0 + 6n2 + -6n2 2 + -7n + 5n2 = 6n2 + -6n2 Combine like terms: 6n2 + -6n2 = 0 2 + -7n + 5n2 = 0 Factor a trinomial. (2 + -5n)(1 + -1n) = 0Subproblem 1
Set the factor '(2 + -5n)' equal to zero and attempt to solve: Simplifying 2 + -5n = 0 Solving 2 + -5n = 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 + -5n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5n = 0 + -2 -5n = 0 + -2 Combine like terms: 0 + -2 = -2 -5n = -2 Divide each side by '-5'. n = 0.4 Simplifying n = 0.4Subproblem 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 = {0.4, 1}
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