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Simplifying (3n + 2)(4n + 5) = 0 Reorder the terms: (2 + 3n)(4n + 5) = 0 Reorder the terms: (2 + 3n)(5 + 4n) = 0 Multiply (2 + 3n) * (5 + 4n) (2(5 + 4n) + 3n * (5 + 4n)) = 0 ((5 * 2 + 4n * 2) + 3n * (5 + 4n)) = 0 ((10 + 8n) + 3n * (5 + 4n)) = 0 (10 + 8n + (5 * 3n + 4n * 3n)) = 0 (10 + 8n + (15n + 12n2)) = 0 Combine like terms: 8n + 15n = 23n (10 + 23n + 12n2) = 0 Solving 10 + 23n + 12n2 = 0 Solving for variable 'n'. Factor a trinomial. (5 + 4n)(2 + 3n) = 0Subproblem 1
Set the factor '(5 + 4n)' equal to zero and attempt to solve: Simplifying 5 + 4n = 0 Solving 5 + 4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4n = 0 + -5 4n = 0 + -5 Combine like terms: 0 + -5 = -5 4n = -5 Divide each side by '4'. n = -1.25 Simplifying n = -1.25Subproblem 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 = {-1.25, -0.6666666667}
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