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Simplifying (5n + 6)(5n + -7) = 0 Reorder the terms: (6 + 5n)(5n + -7) = 0 Reorder the terms: (6 + 5n)(-7 + 5n) = 0 Multiply (6 + 5n) * (-7 + 5n) (6(-7 + 5n) + 5n * (-7 + 5n)) = 0 ((-7 * 6 + 5n * 6) + 5n * (-7 + 5n)) = 0 ((-42 + 30n) + 5n * (-7 + 5n)) = 0 (-42 + 30n + (-7 * 5n + 5n * 5n)) = 0 (-42 + 30n + (-35n + 25n2)) = 0 Combine like terms: 30n + -35n = -5n (-42 + -5n + 25n2) = 0 Solving -42 + -5n + 25n2 = 0 Solving for variable 'n'. Factor a trinomial. (-6 + -5n)(7 + -5n) = 0Subproblem 1
Set the factor '(-6 + -5n)' equal to zero and attempt to solve: Simplifying -6 + -5n = 0 Solving -6 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5n = 0 + 6 -5n = 0 + 6 Combine like terms: 0 + 6 = 6 -5n = 6 Divide each side by '-5'. n = -1.2 Simplifying n = -1.2Subproblem 2
Set the factor '(7 + -5n)' equal to zero and attempt to solve: Simplifying 7 + -5n = 0 Solving 7 + -5n = 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 + -5n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5n = 0 + -7 -5n = 0 + -7 Combine like terms: 0 + -7 = -7 -5n = -7 Divide each side by '-5'. n = 1.4 Simplifying n = 1.4Solution
n = {-1.2, 1.4}
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