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Simplifying (3n + 2)(4n + -5) = 0 Reorder the terms: (2 + 3n)(4n + -5) = 0 Reorder the terms: (2 + 3n)(-5 + 4n) = 0 Multiply (2 + 3n) * (-5 + 4n) (2(-5 + 4n) + 3n * (-5 + 4n)) = 0 ((-5 * 2 + 4n * 2) + 3n * (-5 + 4n)) = 0 ((-10 + 8n) + 3n * (-5 + 4n)) = 0 (-10 + 8n + (-5 * 3n + 4n * 3n)) = 0 (-10 + 8n + (-15n + 12n2)) = 0 Combine like terms: 8n + -15n = -7n (-10 + -7n + 12n2) = 0 Solving -10 + -7n + 12n2 = 0 Solving for variable 'n'. Factor a trinomial. (-2 + -3n)(5 + -4n) = 0Subproblem 1
Set the factor '(-2 + -3n)' equal to zero and attempt to solve: Simplifying -2 + -3n = 0 Solving -2 + -3n = 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 + -3n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3n = 0 + 2 -3n = 0 + 2 Combine like terms: 0 + 2 = 2 -3n = 2 Divide each side by '-3'. n = -0.6666666667 Simplifying n = -0.6666666667Subproblem 2
Set the factor '(5 + -4n)' equal to zero and attempt to solve: Simplifying 5 + -4n = 0 Solving 5 + -4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4n = 0 + -5 -4n = 0 + -5 Combine like terms: 0 + -5 = -5 -4n = -5 Divide each side by '-4'. n = 1.25 Simplifying n = 1.25Solution
n = {-0.6666666667, 1.25}
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