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Simplifying (3n + -2)(4n + -1) = 0 Reorder the terms: (-2 + 3n)(4n + -1) = 0 Reorder the terms: (-2 + 3n)(-1 + 4n) = 0 Multiply (-2 + 3n) * (-1 + 4n) (-2(-1 + 4n) + 3n * (-1 + 4n)) = 0 ((-1 * -2 + 4n * -2) + 3n * (-1 + 4n)) = 0 ((2 + -8n) + 3n * (-1 + 4n)) = 0 (2 + -8n + (-1 * 3n + 4n * 3n)) = 0 (2 + -8n + (-3n + 12n2)) = 0 Combine like terms: -8n + -3n = -11n (2 + -11n + 12n2) = 0 Solving 2 + -11n + 12n2 = 0 Solving for variable 'n'. Factor a trinomial. (1 + -4n)(2 + -3n) = 0Subproblem 1
Set the factor '(1 + -4n)' equal to zero and attempt to solve: Simplifying 1 + -4n = 0 Solving 1 + -4n = 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 + -4n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4n = 0 + -1 -4n = 0 + -1 Combine like terms: 0 + -1 = -1 -4n = -1 Divide each side by '-4'. n = 0.25 Simplifying n = 0.25Subproblem 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 = {0.25, 0.6666666667}
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