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Simplifying 2n2 = -16 + 12n Solving 2n2 = -16 + 12n Solving for variable 'n'. Reorder the terms: 16 + -12n + 2n2 = -16 + 12n + 16 + -12n Reorder the terms: 16 + -12n + 2n2 = -16 + 16 + 12n + -12n Combine like terms: -16 + 16 = 0 16 + -12n + 2n2 = 0 + 12n + -12n 16 + -12n + 2n2 = 12n + -12n Combine like terms: 12n + -12n = 0 16 + -12n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -6n + n2) = 0 Factor a trinomial. 2((2 + -1n)(4 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2Subproblem 2
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 = 4Solution
n = {2, 4}
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