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Simplifying (5n + -4)(3n + 1) = 0 Reorder the terms: (-4 + 5n)(3n + 1) = 0 Reorder the terms: (-4 + 5n)(1 + 3n) = 0 Multiply (-4 + 5n) * (1 + 3n) (-4(1 + 3n) + 5n * (1 + 3n)) = 0 ((1 * -4 + 3n * -4) + 5n * (1 + 3n)) = 0 ((-4 + -12n) + 5n * (1 + 3n)) = 0 (-4 + -12n + (1 * 5n + 3n * 5n)) = 0 (-4 + -12n + (5n + 15n2)) = 0 Combine like terms: -12n + 5n = -7n (-4 + -7n + 15n2) = 0 Solving -4 + -7n + 15n2 = 0 Solving for variable 'n'. Factor a trinomial. (-1 + -3n)(4 + -5n) = 0Subproblem 1
Set the factor '(-1 + -3n)' equal to zero and attempt to solve: Simplifying -1 + -3n = 0 Solving -1 + -3n = 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 + -3n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3n = 0 + 1 -3n = 0 + 1 Combine like terms: 0 + 1 = 1 -3n = 1 Divide each side by '-3'. n = -0.3333333333 Simplifying n = -0.3333333333Subproblem 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 = {-0.3333333333, 0.8}
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