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Simplifying (7n + 4)(n + -7) = 0 Reorder the terms: (4 + 7n)(n + -7) = 0 Reorder the terms: (4 + 7n)(-7 + n) = 0 Multiply (4 + 7n) * (-7 + n) (4(-7 + n) + 7n * (-7 + n)) = 0 ((-7 * 4 + n * 4) + 7n * (-7 + n)) = 0 ((-28 + 4n) + 7n * (-7 + n)) = 0 (-28 + 4n + (-7 * 7n + n * 7n)) = 0 (-28 + 4n + (-49n + 7n2)) = 0 Combine like terms: 4n + -49n = -45n (-28 + -45n + 7n2) = 0 Solving -28 + -45n + 7n2 = 0 Solving for variable 'n'. Factor a trinomial. (-4 + -7n)(7 + -1n) = 0Subproblem 1
Set the factor '(-4 + -7n)' equal to zero and attempt to solve: Simplifying -4 + -7n = 0 Solving -4 + -7n = 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 + -7n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7n = 0 + 4 -7n = 0 + 4 Combine like terms: 0 + 4 = 4 -7n = 4 Divide each side by '-7'. n = -0.5714285714 Simplifying n = -0.5714285714Subproblem 2
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 = 7Solution
n = {-0.5714285714, 7}
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