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Simplifying (n + -7)(3n + -2) = 0 Reorder the terms: (-7 + n)(3n + -2) = 0 Reorder the terms: (-7 + n)(-2 + 3n) = 0 Multiply (-7 + n) * (-2 + 3n) (-7(-2 + 3n) + n(-2 + 3n)) = 0 ((-2 * -7 + 3n * -7) + n(-2 + 3n)) = 0 ((14 + -21n) + n(-2 + 3n)) = 0 (14 + -21n + (-2 * n + 3n * n)) = 0 (14 + -21n + (-2n + 3n2)) = 0 Combine like terms: -21n + -2n = -23n (14 + -23n + 3n2) = 0 Solving 14 + -23n + 3n2 = 0 Solving for variable 'n'. Factor a trinomial. (2 + -3n)(7 + -1n) = 0Subproblem 1
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 = 0.6666666667Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 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 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {0.6666666667, 7}
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