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Simplifying (6n + 1)(5n + -3) = 0 Reorder the terms: (1 + 6n)(5n + -3) = 0 Reorder the terms: (1 + 6n)(-3 + 5n) = 0 Multiply (1 + 6n) * (-3 + 5n) (1(-3 + 5n) + 6n * (-3 + 5n)) = 0 ((-3 * 1 + 5n * 1) + 6n * (-3 + 5n)) = 0 ((-3 + 5n) + 6n * (-3 + 5n)) = 0 (-3 + 5n + (-3 * 6n + 5n * 6n)) = 0 (-3 + 5n + (-18n + 30n2)) = 0 Combine like terms: 5n + -18n = -13n (-3 + -13n + 30n2) = 0 Solving -3 + -13n + 30n2 = 0 Solving for variable 'n'. Factor a trinomial. (-1 + -6n)(3 + -5n) = 0Subproblem 1
Set the factor '(-1 + -6n)' equal to zero and attempt to solve: Simplifying -1 + -6n = 0 Solving -1 + -6n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -6n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6n = 0 + 1 -6n = 0 + 1 Combine like terms: 0 + 1 = 1 -6n = 1 Divide each side by '-6'. n = -0.1666666667 Simplifying n = -0.1666666667Subproblem 2
Set the factor '(3 + -5n)' equal to zero and attempt to solve: Simplifying 3 + -5n = 0 Solving 3 + -5n = 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 + -5n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5n = 0 + -3 -5n = 0 + -3 Combine like terms: 0 + -3 = -3 -5n = -3 Divide each side by '-5'. n = 0.6 Simplifying n = 0.6Solution
n = {-0.1666666667, 0.6}
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