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Simplifying (1 + -4n)(2 + -3n) = 0 Multiply (1 + -4n) * (2 + -3n) (1(2 + -3n) + -4n * (2 + -3n)) = 0 ((2 * 1 + -3n * 1) + -4n * (2 + -3n)) = 0 ((2 + -3n) + -4n * (2 + -3n)) = 0 (2 + -3n + (2 * -4n + -3n * -4n)) = 0 (2 + -3n + (-8n + 12n2)) = 0 Combine like terms: -3n + -8n = -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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