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Simplifying (5n + -2) * 3n + -1(5n + -2)(n + -1) = 0 Reorder the terms: (-2 + 5n) * 3n + -1(5n + -2)(n + -1) = 0 Reorder the terms for easier multiplication: 3n(-2 + 5n) + -1(5n + -2)(n + -1) = 0 (-2 * 3n + 5n * 3n) + -1(5n + -2)(n + -1) = 0 (-6n + 15n2) + -1(5n + -2)(n + -1) = 0 Reorder the terms: -6n + 15n2 + -1(-2 + 5n)(n + -1) = 0 Reorder the terms: -6n + 15n2 + -1(-2 + 5n)(-1 + n) = 0 Multiply (-2 + 5n) * (-1 + n) -6n + 15n2 + -1(-2(-1 + n) + 5n * (-1 + n)) = 0 -6n + 15n2 + -1((-1 * -2 + n * -2) + 5n * (-1 + n)) = 0 -6n + 15n2 + -1((2 + -2n) + 5n * (-1 + n)) = 0 -6n + 15n2 + -1(2 + -2n + (-1 * 5n + n * 5n)) = 0 -6n + 15n2 + -1(2 + -2n + (-5n + 5n2)) = 0 Combine like terms: -2n + -5n = -7n -6n + 15n2 + -1(2 + -7n + 5n2) = 0 -6n + 15n2 + (2 * -1 + -7n * -1 + 5n2 * -1) = 0 -6n + 15n2 + (-2 + 7n + -5n2) = 0 Reorder the terms: -2 + -6n + 7n + 15n2 + -5n2 = 0 Combine like terms: -6n + 7n = 1n -2 + 1n + 15n2 + -5n2 = 0 Combine like terms: 15n2 + -5n2 = 10n2 -2 + 1n + 10n2 = 0 Solving -2 + 1n + 10n2 = 0 Solving for variable 'n'. Factor a trinomial. (-1 + -2n)(2 + -5n) = 0Subproblem 1
Set the factor '(-1 + -2n)' equal to zero and attempt to solve: Simplifying -1 + -2n = 0 Solving -1 + -2n = 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 + -2n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2n = 0 + 1 -2n = 0 + 1 Combine like terms: 0 + 1 = 1 -2n = 1 Divide each side by '-2'. n = -0.5 Simplifying n = -0.5Subproblem 2
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 = 0.4Solution
n = {-0.5, 0.4}
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