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Simplifying n2 = 6n + 72 Reorder the terms: n2 = 72 + 6n Solving n2 = 72 + 6n Solving for variable 'n'. Reorder the terms: -72 + -6n + n2 = 72 + 6n + -72 + -6n Reorder the terms: -72 + -6n + n2 = 72 + -72 + 6n + -6n Combine like terms: 72 + -72 = 0 -72 + -6n + n2 = 0 + 6n + -6n -72 + -6n + n2 = 6n + -6n Combine like terms: 6n + -6n = 0 -72 + -6n + n2 = 0 Factor a trinomial. (-6 + -1n)(12 + -1n) = 0Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve: Simplifying -6 + -1n = 0 Solving -6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1n = 0 + 6 -1n = 0 + 6 Combine like terms: 0 + 6 = 6 -1n = 6 Divide each side by '-1'. n = -6 Simplifying n = -6Subproblem 2
Set the factor '(12 + -1n)' equal to zero and attempt to solve: Simplifying 12 + -1n = 0 Solving 12 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1n = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1n = 0 + -12 -1n = 0 + -12 Combine like terms: 0 + -12 = -12 -1n = -12 Divide each side by '-1'. n = 12 Simplifying n = 12Solution
n = {-6, 12}
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