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Simplifying (n2) + -12 + 4n + 11 = 76 n2 + -12 + 4n + 11 = 76 Reorder the terms: -12 + 11 + 4n + n2 = 76 Combine like terms: -12 + 11 = -1 -1 + 4n + n2 = 76 Solving -1 + 4n + n2 = 76 Solving for variable 'n'. Reorder the terms: -1 + -76 + 4n + n2 = 76 + -76 Combine like terms: -1 + -76 = -77 -77 + 4n + n2 = 76 + -76 Combine like terms: 76 + -76 = 0 -77 + 4n + n2 = 0 Factor a trinomial. (-11 + -1n)(7 + -1n) = 0Subproblem 1
Set the factor '(-11 + -1n)' equal to zero and attempt to solve: Simplifying -11 + -1n = 0 Solving -11 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1n = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1n = 0 + 11 -1n = 0 + 11 Combine like terms: 0 + 11 = 11 -1n = 11 Divide each side by '-1'. n = -11 Simplifying n = -11Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {-11, 7}
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