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Simplifying (3n + -2)(5n + 4) = 0 Reorder the terms: (-2 + 3n)(5n + 4) = 0 Reorder the terms: (-2 + 3n)(4 + 5n) = 0 Multiply (-2 + 3n) * (4 + 5n) (-2(4 + 5n) + 3n * (4 + 5n)) = 0 ((4 * -2 + 5n * -2) + 3n * (4 + 5n)) = 0 ((-8 + -10n) + 3n * (4 + 5n)) = 0 (-8 + -10n + (4 * 3n + 5n * 3n)) = 0 (-8 + -10n + (12n + 15n2)) = 0 Combine like terms: -10n + 12n = 2n (-8 + 2n + 15n2) = 0 Solving -8 + 2n + 15n2 = 0 Solving for variable 'n'. Factor a trinomial. (-4 + -5n)(2 + -3n) = 0Subproblem 1
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 = -0.8Subproblem 2
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 = 0.6666666667Solution
n = {-0.8, 0.6666666667}
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