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Simplifying n2 = -32 + 12n Solving n2 = -32 + 12n Solving for variable 'n'. Reorder the terms: 32 + -12n + n2 = -32 + 12n + 32 + -12n Reorder the terms: 32 + -12n + n2 = -32 + 32 + 12n + -12n Combine like terms: -32 + 32 = 0 32 + -12n + n2 = 0 + 12n + -12n 32 + -12n + n2 = 12n + -12n Combine like terms: 12n + -12n = 0 32 + -12n + n2 = 0 Factor a trinomial. (4 + -1n)(8 + -1n) = 0Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Subproblem 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 = {4, 8}
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