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Simplifying (3n + 7)(5n + -4) = 0 Reorder the terms: (7 + 3n)(5n + -4) = 0 Reorder the terms: (7 + 3n)(-4 + 5n) = 0 Multiply (7 + 3n) * (-4 + 5n) (7(-4 + 5n) + 3n * (-4 + 5n)) = 0 ((-4 * 7 + 5n * 7) + 3n * (-4 + 5n)) = 0 ((-28 + 35n) + 3n * (-4 + 5n)) = 0 (-28 + 35n + (-4 * 3n + 5n * 3n)) = 0 (-28 + 35n + (-12n + 15n2)) = 0 Combine like terms: 35n + -12n = 23n (-28 + 23n + 15n2) = 0 Solving -28 + 23n + 15n2 = 0 Solving for variable 'n'. Factor a trinomial. (-7 + -3n)(4 + -5n) = 0Subproblem 1
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 = -2.333333333Subproblem 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 = {-2.333333333, 0.8}
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