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Simplifying 12n2 + -45n + 21 = 7n + 5 Reorder the terms: 21 + -45n + 12n2 = 7n + 5 Reorder the terms: 21 + -45n + 12n2 = 5 + 7n Solving 21 + -45n + 12n2 = 5 + 7n Solving for variable 'n'. Reorder the terms: 21 + -5 + -45n + -7n + 12n2 = 5 + 7n + -5 + -7n Combine like terms: 21 + -5 = 16 16 + -45n + -7n + 12n2 = 5 + 7n + -5 + -7n Combine like terms: -45n + -7n = -52n 16 + -52n + 12n2 = 5 + 7n + -5 + -7n Reorder the terms: 16 + -52n + 12n2 = 5 + -5 + 7n + -7n Combine like terms: 5 + -5 = 0 16 + -52n + 12n2 = 0 + 7n + -7n 16 + -52n + 12n2 = 7n + -7n Combine like terms: 7n + -7n = 0 16 + -52n + 12n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(4 + -13n + 3n2) = 0 Factor a trinomial. 4((1 + -3n)(4 + -1n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -3n)' equal to zero and attempt to solve: Simplifying 1 + -3n = 0 Solving 1 + -3n = 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 + -3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3n = 0 + -1 -3n = 0 + -1 Combine like terms: 0 + -1 = -1 -3n = -1 Divide each side by '-3'. n = 0.3333333333 Simplifying n = 0.3333333333Subproblem 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 = {0.3333333333, 4}
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