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Simplifying (7n + -2)(5n + -4) = 0 Reorder the terms: (-2 + 7n)(5n + -4) = 0 Reorder the terms: (-2 + 7n)(-4 + 5n) = 0 Multiply (-2 + 7n) * (-4 + 5n) (-2(-4 + 5n) + 7n * (-4 + 5n)) = 0 ((-4 * -2 + 5n * -2) + 7n * (-4 + 5n)) = 0 ((8 + -10n) + 7n * (-4 + 5n)) = 0 (8 + -10n + (-4 * 7n + 5n * 7n)) = 0 (8 + -10n + (-28n + 35n2)) = 0 Combine like terms: -10n + -28n = -38n (8 + -38n + 35n2) = 0 Solving 8 + -38n + 35n2 = 0 Solving for variable 'n'. Factor a trinomial. (2 + -7n)(4 + -5n) = 0Subproblem 1
Set the factor '(2 + -7n)' equal to zero and attempt to solve: Simplifying 2 + -7n = 0 Solving 2 + -7n = 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 + -7n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7n = 0 + -2 -7n = 0 + -2 Combine like terms: 0 + -2 = -2 -7n = -2 Divide each side by '-7'. n = 0.2857142857 Simplifying n = 0.2857142857Subproblem 2
Set the factor '(4 + -5n)' equal to zero and attempt to solve: Simplifying 4 + -5n = 0 Solving 4 + -5n = 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 + -5n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5n = 0 + -4 -5n = 0 + -4 Combine like terms: 0 + -4 = -4 -5n = -4 Divide each side by '-5'. n = 0.8 Simplifying n = 0.8Solution
n = {0.2857142857, 0.8}
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