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Simplifying 21n2 + -27 = 7n + 1 Reorder the terms: -27 + 21n2 = 7n + 1 Reorder the terms: -27 + 21n2 = 1 + 7n Solving -27 + 21n2 = 1 + 7n Solving for variable 'n'. Reorder the terms: -27 + -1 + -7n + 21n2 = 1 + 7n + -1 + -7n Combine like terms: -27 + -1 = -28 -28 + -7n + 21n2 = 1 + 7n + -1 + -7n Reorder the terms: -28 + -7n + 21n2 = 1 + -1 + 7n + -7n Combine like terms: 1 + -1 = 0 -28 + -7n + 21n2 = 0 + 7n + -7n -28 + -7n + 21n2 = 7n + -7n Combine like terms: 7n + -7n = 0 -28 + -7n + 21n2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-4 + -1n + 3n2) = 0 Factor a trinomial. 7((-1 + -1n)(4 + -3n)) = 0 Ignore the factor 7.Subproblem 1
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 = -1Subproblem 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 = {-1, 1.333333333}
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