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Simplifying 20n2 + -3n = 5n2 + 3 + -7n Reorder the terms: -3n + 20n2 = 5n2 + 3 + -7n Reorder the terms: -3n + 20n2 = 3 + -7n + 5n2 Solving -3n + 20n2 = 3 + -7n + 5n2 Solving for variable 'n'. Reorder the terms: -3 + -3n + 7n + 20n2 + -5n2 = 3 + -7n + 5n2 + -3 + 7n + -5n2 Combine like terms: -3n + 7n = 4n -3 + 4n + 20n2 + -5n2 = 3 + -7n + 5n2 + -3 + 7n + -5n2 Combine like terms: 20n2 + -5n2 = 15n2 -3 + 4n + 15n2 = 3 + -7n + 5n2 + -3 + 7n + -5n2 Reorder the terms: -3 + 4n + 15n2 = 3 + -3 + -7n + 7n + 5n2 + -5n2 Combine like terms: 3 + -3 = 0 -3 + 4n + 15n2 = 0 + -7n + 7n + 5n2 + -5n2 -3 + 4n + 15n2 = -7n + 7n + 5n2 + -5n2 Combine like terms: -7n + 7n = 0 -3 + 4n + 15n2 = 0 + 5n2 + -5n2 -3 + 4n + 15n2 = 5n2 + -5n2 Combine like terms: 5n2 + -5n2 = 0 -3 + 4n + 15n2 = 0 Factor a trinomial. (-3 + -5n)(1 + -3n) = 0Subproblem 1
Set the factor '(-3 + -5n)' equal to zero and attempt to solve: Simplifying -3 + -5n = 0 Solving -3 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -5n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5n = 0 + 3 -5n = 0 + 3 Combine like terms: 0 + 3 = 3 -5n = 3 Divide each side by '-5'. n = -0.6 Simplifying n = -0.6Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve: Simplifying 1 + -3n = 0 Solving 1 + -3n = 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 + -3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3n = 0 + -1 -3n = 0 + -1 Combine like terms: 0 + -1 = -1 -3n = -1 Divide each side by '-3'. n = 0.3333333333 Simplifying n = 0.3333333333Solution
n = {-0.6, 0.3333333333}
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