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Simplifying n(5n + -2)(5n + 2) = 0 Reorder the terms: n(-2 + 5n)(5n + 2) = 0 Reorder the terms: n(-2 + 5n)(2 + 5n) = 0 Multiply (-2 + 5n) * (2 + 5n) n(-2(2 + 5n) + 5n * (2 + 5n)) = 0 n((2 * -2 + 5n * -2) + 5n * (2 + 5n)) = 0 n((-4 + -10n) + 5n * (2 + 5n)) = 0 n(-4 + -10n + (2 * 5n + 5n * 5n)) = 0 n(-4 + -10n + (10n + 25n2)) = 0 Combine like terms: -10n + 10n = 0 n(-4 + 0 + 25n2) = 0 n(-4 + 25n2) = 0 (-4 * n + 25n2 * n) = 0 (-4n + 25n3) = 0 Solving -4n + 25n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(-4 + 25n2) = 0 Factor a difference between two squares. n((2 + 5n)(-2 + 5n)) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 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 = -0.4Subproblem 3
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, -0.4, 0.4}
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