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Simplifying (n + 4)(3n + -7) = 0 Reorder the terms: (4 + n)(3n + -7) = 0 Reorder the terms: (4 + n)(-7 + 3n) = 0 Multiply (4 + n) * (-7 + 3n) (4(-7 + 3n) + n(-7 + 3n)) = 0 ((-7 * 4 + 3n * 4) + n(-7 + 3n)) = 0 ((-28 + 12n) + n(-7 + 3n)) = 0 (-28 + 12n + (-7 * n + 3n * n)) = 0 (-28 + 12n + (-7n + 3n2)) = 0 Combine like terms: 12n + -7n = 5n (-28 + 5n + 3n2) = 0 Solving -28 + 5n + 3n2 = 0 Solving for variable 'n'. Factor a trinomial. (-4 + -1n)(7 + -3n) = 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 '(7 + -3n)' equal to zero and attempt to solve: Simplifying 7 + -3n = 0 Solving 7 + -3n = 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 + -3n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3n = 0 + -7 -3n = 0 + -7 Combine like terms: 0 + -7 = -7 -3n = -7 Divide each side by '-3'. n = 2.333333333 Simplifying n = 2.333333333Solution
n = {-4, 2.333333333}
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