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Simplifying 21n2 + 14n + -53 = 3 Reorder the terms: -53 + 14n + 21n2 = 3 Solving -53 + 14n + 21n2 = 3 Solving for variable 'n'. Reorder the terms: -53 + -3 + 14n + 21n2 = 3 + -3 Combine like terms: -53 + -3 = -56 -56 + 14n + 21n2 = 3 + -3 Combine like terms: 3 + -3 = 0 -56 + 14n + 21n2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-8 + 2n + 3n2) = 0 Factor a trinomial. 7((-2 + -1n)(4 + -3n)) = 0 Ignore the factor 7.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 + -3n)' equal to zero and attempt to solve: Simplifying 4 + -3n = 0 Solving 4 + -3n = 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 + -3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3n = 0 + -4 -3n = 0 + -4 Combine like terms: 0 + -4 = -4 -3n = -4 Divide each side by '-3'. n = 1.333333333 Simplifying n = 1.333333333Solution
n = {-2, 1.333333333}
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