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Simplifying (8n + 7)(6n + -7) = 0 Reorder the terms: (7 + 8n)(6n + -7) = 0 Reorder the terms: (7 + 8n)(-7 + 6n) = 0 Multiply (7 + 8n) * (-7 + 6n) (7(-7 + 6n) + 8n * (-7 + 6n)) = 0 ((-7 * 7 + 6n * 7) + 8n * (-7 + 6n)) = 0 ((-49 + 42n) + 8n * (-7 + 6n)) = 0 (-49 + 42n + (-7 * 8n + 6n * 8n)) = 0 (-49 + 42n + (-56n + 48n2)) = 0 Combine like terms: 42n + -56n = -14n (-49 + -14n + 48n2) = 0 Solving -49 + -14n + 48n2 = 0 Solving for variable 'n'. Factor a trinomial. (-7 + -8n)(7 + -6n) = 0Subproblem 1
Set the factor '(-7 + -8n)' equal to zero and attempt to solve: Simplifying -7 + -8n = 0 Solving -7 + -8n = 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 + -8n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8n = 0 + 7 -8n = 0 + 7 Combine like terms: 0 + 7 = 7 -8n = 7 Divide each side by '-8'. n = -0.875 Simplifying n = -0.875Subproblem 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 = {-0.875, 1.166666667}
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