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Simplifying (2n + 7)(6n + 4) = 0 Reorder the terms: (7 + 2n)(6n + 4) = 0 Reorder the terms: (7 + 2n)(4 + 6n) = 0 Multiply (7 + 2n) * (4 + 6n) (7(4 + 6n) + 2n * (4 + 6n)) = 0 ((4 * 7 + 6n * 7) + 2n * (4 + 6n)) = 0 ((28 + 42n) + 2n * (4 + 6n)) = 0 (28 + 42n + (4 * 2n + 6n * 2n)) = 0 (28 + 42n + (8n + 12n2)) = 0 Combine like terms: 42n + 8n = 50n (28 + 50n + 12n2) = 0 Solving 28 + 50n + 12n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 25n + 6n2) = 0 Factor a trinomial. 2((7 + 2n)(2 + 3n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 2n)' equal to zero and attempt to solve: Simplifying 7 + 2n = 0 Solving 7 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2n = 0 + -7 2n = 0 + -7 Combine like terms: 0 + -7 = -7 2n = -7 Divide each side by '2'. n = -3.5 Simplifying n = -3.5Subproblem 2
Set the factor '(2 + 3n)' equal to zero and attempt to solve: Simplifying 2 + 3n = 0 Solving 2 + 3n = 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 + 3n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3n = 0 + -2 3n = 0 + -2 Combine like terms: 0 + -2 = -2 3n = -2 Divide each side by '3'. n = -0.6666666667 Simplifying n = -0.6666666667Solution
n = {-3.5, -0.6666666667}
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