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Simplifying (n + 4)(5n + -1) = 0 Reorder the terms: (4 + n)(5n + -1) = 0 Reorder the terms: (4 + n)(-1 + 5n) = 0 Multiply (4 + n) * (-1 + 5n) (4(-1 + 5n) + n(-1 + 5n)) = 0 ((-1 * 4 + 5n * 4) + n(-1 + 5n)) = 0 ((-4 + 20n) + n(-1 + 5n)) = 0 (-4 + 20n + (-1 * n + 5n * n)) = 0 (-4 + 20n + (-1n + 5n2)) = 0 Combine like terms: 20n + -1n = 19n (-4 + 19n + 5n2) = 0 Solving -4 + 19n + 5n2 = 0 Solving for variable 'n'. Factor a trinomial. (-4 + -1n)(1 + -5n) = 0Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve: Simplifying -4 + -1n = 0 Solving -4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1n = 0 + 4 -1n = 0 + 4 Combine like terms: 0 + 4 = 4 -1n = 4 Divide each side by '-1'. n = -4 Simplifying n = -4Subproblem 2
Set the factor '(1 + -5n)' equal to zero and attempt to solve: Simplifying 1 + -5n = 0 Solving 1 + -5n = 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 + -5n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5n = 0 + -1 -5n = 0 + -1 Combine like terms: 0 + -1 = -1 -5n = -1 Divide each side by '-5'. n = 0.2 Simplifying n = 0.2Solution
n = {-4, 0.2}
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