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Simplifying 5n2 = 3n + 2 Reorder the terms: 5n2 = 2 + 3n Solving 5n2 = 2 + 3n Solving for variable 'n'. Reorder the terms: -2 + -3n + 5n2 = 2 + 3n + -2 + -3n Reorder the terms: -2 + -3n + 5n2 = 2 + -2 + 3n + -3n Combine like terms: 2 + -2 = 0 -2 + -3n + 5n2 = 0 + 3n + -3n -2 + -3n + 5n2 = 3n + -3n Combine like terms: 3n + -3n = 0 -2 + -3n + 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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