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Simplifying (7n + 3)(5n + -6) = 0 Reorder the terms: (3 + 7n)(5n + -6) = 0 Reorder the terms: (3 + 7n)(-6 + 5n) = 0 Multiply (3 + 7n) * (-6 + 5n) (3(-6 + 5n) + 7n * (-6 + 5n)) = 0 ((-6 * 3 + 5n * 3) + 7n * (-6 + 5n)) = 0 ((-18 + 15n) + 7n * (-6 + 5n)) = 0 (-18 + 15n + (-6 * 7n + 5n * 7n)) = 0 (-18 + 15n + (-42n + 35n2)) = 0 Combine like terms: 15n + -42n = -27n (-18 + -27n + 35n2) = 0 Solving -18 + -27n + 35n2 = 0 Solving for variable 'n'. Factor a trinomial. (-3 + -7n)(6 + -5n) = 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 '(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 = 1.2Solution
n = {-0.4285714286, 1.2}
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