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Simplifying (5n + -1)(n + 7) = 0 Reorder the terms: (-1 + 5n)(n + 7) = 0 Reorder the terms: (-1 + 5n)(7 + n) = 0 Multiply (-1 + 5n) * (7 + n) (-1(7 + n) + 5n * (7 + n)) = 0 ((7 * -1 + n * -1) + 5n * (7 + n)) = 0 ((-7 + -1n) + 5n * (7 + n)) = 0 (-7 + -1n + (7 * 5n + n * 5n)) = 0 (-7 + -1n + (35n + 5n2)) = 0 Combine like terms: -1n + 35n = 34n (-7 + 34n + 5n2) = 0 Solving -7 + 34n + 5n2 = 0 Solving for variable 'n'. Factor a trinomial. (-7 + -1n)(1 + -5n) = 0Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve: Simplifying -7 + -1n = 0 Solving -7 + -1n = 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 + -1n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1n = 0 + 7 -1n = 0 + 7 Combine like terms: 0 + 7 = 7 -1n = 7 Divide each side by '-1'. n = -7 Simplifying n = -7Subproblem 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 = {-7, 0.2}
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