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Simplifying 3n2 + 12n + -8 = 7 Reorder the terms: -8 + 12n + 3n2 = 7 Solving -8 + 12n + 3n2 = 7 Solving for variable 'n'. Reorder the terms: -8 + -7 + 12n + 3n2 = 7 + -7 Combine like terms: -8 + -7 = -15 -15 + 12n + 3n2 = 7 + -7 Combine like terms: 7 + -7 = 0 -15 + 12n + 3n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 4n + n2) = 0 Factor a trinomial. 3((-5 + -1n)(1 + -1n)) = 0 Ignore the factor 3.Subproblem 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 '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Solution
n = {-5, 1}
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