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Simplifying (7n + -3)(6n + -7) = 0 Reorder the terms: (-3 + 7n)(6n + -7) = 0 Reorder the terms: (-3 + 7n)(-7 + 6n) = 0 Multiply (-3 + 7n) * (-7 + 6n) (-3(-7 + 6n) + 7n * (-7 + 6n)) = 0 ((-7 * -3 + 6n * -3) + 7n * (-7 + 6n)) = 0 ((21 + -18n) + 7n * (-7 + 6n)) = 0 (21 + -18n + (-7 * 7n + 6n * 7n)) = 0 (21 + -18n + (-49n + 42n2)) = 0 Combine like terms: -18n + -49n = -67n (21 + -67n + 42n2) = 0 Solving 21 + -67n + 42n2 = 0 Solving for variable 'n'. Factor a trinomial. (3 + -7n)(7 + -6n) = 0Subproblem 1
Set the factor '(3 + -7n)' equal to zero and attempt to solve: Simplifying 3 + -7n = 0 Solving 3 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -7n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7n = 0 + -3 -7n = 0 + -3 Combine like terms: 0 + -3 = -3 -7n = -3 Divide each side by '-7'. n = 0.4285714286 Simplifying n = 0.4285714286Subproblem 2
Set the factor '(7 + -6n)' equal to zero and attempt to solve: Simplifying 7 + -6n = 0 Solving 7 + -6n = 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 + -6n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6n = 0 + -7 -6n = 0 + -7 Combine like terms: 0 + -7 = -7 -6n = -7 Divide each side by '-6'. n = 1.166666667 Simplifying n = 1.166666667Solution
n = {0.4285714286, 1.166666667}
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