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Simplifying 3n2 = 40 + 7n Solving 3n2 = 40 + 7n Solving for variable 'n'. Reorder the terms: -40 + -7n + 3n2 = 40 + 7n + -40 + -7n Reorder the terms: -40 + -7n + 3n2 = 40 + -40 + 7n + -7n Combine like terms: 40 + -40 = 0 -40 + -7n + 3n2 = 0 + 7n + -7n -40 + -7n + 3n2 = 7n + -7n Combine like terms: 7n + -7n = 0 -40 + -7n + 3n2 = 0 Factor a trinomial. (-8 + -3n)(5 + -1n) = 0Subproblem 1
Set the factor '(-8 + -3n)' equal to zero and attempt to solve: Simplifying -8 + -3n = 0 Solving -8 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3n = 0 + 8 -3n = 0 + 8 Combine like terms: 0 + 8 = 8 -3n = 8 Divide each side by '-3'. n = -2.666666667 Simplifying n = -2.666666667Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 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 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {-2.666666667, 5}
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