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Simplifying (5n + 2)(2n + -3) = 0 Reorder the terms: (2 + 5n)(2n + -3) = 0 Reorder the terms: (2 + 5n)(-3 + 2n) = 0 Multiply (2 + 5n) * (-3 + 2n) (2(-3 + 2n) + 5n * (-3 + 2n)) = 0 ((-3 * 2 + 2n * 2) + 5n * (-3 + 2n)) = 0 ((-6 + 4n) + 5n * (-3 + 2n)) = 0 (-6 + 4n + (-3 * 5n + 2n * 5n)) = 0 (-6 + 4n + (-15n + 10n2)) = 0 Combine like terms: 4n + -15n = -11n (-6 + -11n + 10n2) = 0 Solving -6 + -11n + 10n2 = 0 Solving for variable 'n'. Factor a trinomial. (-2 + -5n)(3 + -2n) = 0Subproblem 1
Set the factor '(-2 + -5n)' equal to zero and attempt to solve: Simplifying -2 + -5n = 0 Solving -2 + -5n = 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 + -5n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5n = 0 + 2 -5n = 0 + 2 Combine like terms: 0 + 2 = 2 -5n = 2 Divide each side by '-5'. n = -0.4 Simplifying n = -0.4Subproblem 2
Set the factor '(3 + -2n)' equal to zero and attempt to solve: Simplifying 3 + -2n = 0 Solving 3 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2n = 0 + -3 -2n = 0 + -3 Combine like terms: 0 + -3 = -3 -2n = -3 Divide each side by '-2'. n = 1.5 Simplifying n = 1.5Solution
n = {-0.4, 1.5}
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