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Simplifying (7n + 2)(2n + -7) = 0 Reorder the terms: (2 + 7n)(2n + -7) = 0 Reorder the terms: (2 + 7n)(-7 + 2n) = 0 Multiply (2 + 7n) * (-7 + 2n) (2(-7 + 2n) + 7n * (-7 + 2n)) = 0 ((-7 * 2 + 2n * 2) + 7n * (-7 + 2n)) = 0 ((-14 + 4n) + 7n * (-7 + 2n)) = 0 (-14 + 4n + (-7 * 7n + 2n * 7n)) = 0 (-14 + 4n + (-49n + 14n2)) = 0 Combine like terms: 4n + -49n = -45n (-14 + -45n + 14n2) = 0 Solving -14 + -45n + 14n2 = 0 Solving for variable 'n'. Factor a trinomial. (-2 + -7n)(7 + -2n) = 0Subproblem 1
Set the factor '(-2 + -7n)' equal to zero and attempt to solve: Simplifying -2 + -7n = 0 Solving -2 + -7n = 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 + -7n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7n = 0 + 2 -7n = 0 + 2 Combine like terms: 0 + 2 = 2 -7n = 2 Divide each side by '-7'. n = -0.2857142857 Simplifying n = -0.2857142857Subproblem 2
Set the factor '(7 + -2n)' equal to zero and attempt to solve: Simplifying 7 + -2n = 0 Solving 7 + -2n = 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 + -2n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2n = 0 + -7 -2n = 0 + -7 Combine like terms: 0 + -7 = -7 -2n = -7 Divide each side by '-2'. n = 3.5 Simplifying n = 3.5Solution
n = {-0.2857142857, 3.5}
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