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