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Simplifying (5n + 2)(n + -6) = 0 Reorder the terms: (2 + 5n)(n + -6) = 0 Reorder the terms: (2 + 5n)(-6 + n) = 0 Multiply (2 + 5n) * (-6 + n) (2(-6 + n) + 5n * (-6 + n)) = 0 ((-6 * 2 + n * 2) + 5n * (-6 + n)) = 0 ((-12 + 2n) + 5n * (-6 + n)) = 0 (-12 + 2n + (-6 * 5n + n * 5n)) = 0 (-12 + 2n + (-30n + 5n2)) = 0 Combine like terms: 2n + -30n = -28n (-12 + -28n + 5n2) = 0 Solving -12 + -28n + 5n2 = 0 Solving for variable 'n'. Factor a trinomial. (-2 + -5n)(6 + -1n) = 0Subproblem 1
Set the factor '(-2 + -5n)' equal to zero and attempt to solve: Simplifying -2 + -5n = 0 Solving -2 + -5n = 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 + -5n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5n = 0 + 2 -5n = 0 + 2 Combine like terms: 0 + 2 = 2 -5n = 2 Divide each side by '-5'. n = -0.4 Simplifying n = -0.4Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 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 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6Solution
n = {-0.4, 6}
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