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Simplifying 7n2 + -6n + -5 = (3n + 1)(4n + 1) Reorder the terms: -5 + -6n + 7n2 = (3n + 1)(4n + 1) Reorder the terms: -5 + -6n + 7n2 = (1 + 3n)(4n + 1) Reorder the terms: -5 + -6n + 7n2 = (1 + 3n)(1 + 4n) Multiply (1 + 3n) * (1 + 4n) -5 + -6n + 7n2 = (1(1 + 4n) + 3n * (1 + 4n)) -5 + -6n + 7n2 = ((1 * 1 + 4n * 1) + 3n * (1 + 4n)) -5 + -6n + 7n2 = ((1 + 4n) + 3n * (1 + 4n)) -5 + -6n + 7n2 = (1 + 4n + (1 * 3n + 4n * 3n)) -5 + -6n + 7n2 = (1 + 4n + (3n + 12n2)) Combine like terms: 4n + 3n = 7n -5 + -6n + 7n2 = (1 + 7n + 12n2) Solving -5 + -6n + 7n2 = 1 + 7n + 12n2 Solving for variable 'n'. Reorder the terms: -5 + -1 + -6n + -7n + 7n2 + -12n2 = 1 + 7n + 12n2 + -1 + -7n + -12n2 Combine like terms: -5 + -1 = -6 -6 + -6n + -7n + 7n2 + -12n2 = 1 + 7n + 12n2 + -1 + -7n + -12n2 Combine like terms: -6n + -7n = -13n -6 + -13n + 7n2 + -12n2 = 1 + 7n + 12n2 + -1 + -7n + -12n2 Combine like terms: 7n2 + -12n2 = -5n2 -6 + -13n + -5n2 = 1 + 7n + 12n2 + -1 + -7n + -12n2 Reorder the terms: -6 + -13n + -5n2 = 1 + -1 + 7n + -7n + 12n2 + -12n2 Combine like terms: 1 + -1 = 0 -6 + -13n + -5n2 = 0 + 7n + -7n + 12n2 + -12n2 -6 + -13n + -5n2 = 7n + -7n + 12n2 + -12n2 Combine like terms: 7n + -7n = 0 -6 + -13n + -5n2 = 0 + 12n2 + -12n2 -6 + -13n + -5n2 = 12n2 + -12n2 Combine like terms: 12n2 + -12n2 = 0 -6 + -13n + -5n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 13n + 5n2) = 0 Factor a trinomial. -1((2 + n)(3 + 5n)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 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 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Subproblem 2
Set the factor '(3 + 5n)' equal to zero and attempt to solve: Simplifying 3 + 5n = 0 Solving 3 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 5n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5n = 0 + -3 5n = 0 + -3 Combine like terms: 0 + -3 = -3 5n = -3 Divide each side by '5'. n = -0.6 Simplifying n = -0.6Solution
n = {-2, -0.6}
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