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Simplifying 2n2(n + -10) = -42n Reorder the terms: 2n2(-10 + n) = -42n (-10 * 2n2 + n * 2n2) = -42n (-20n2 + 2n3) = -42n Solving -20n2 + 2n3 = -42n Solving for variable 'n'. Reorder the terms: 42n + -20n2 + 2n3 = -42n + 42n Combine like terms: -42n + 42n = 0 42n + -20n2 + 2n3 = 0 Factor out the Greatest Common Factor (GCF), '2n'. 2n(21 + -10n + n2) = 0 Factor a trinomial. 2n((3 + -1n)(7 + -1n)) = 0 Ignore the factor 2.Subproblem 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 '(3 + -1n)' equal to zero and attempt to solve: Simplifying 3 + -1n = 0 Solving 3 + -1n = 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 + -1n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n = 0 + -3 -1n = 0 + -3 Combine like terms: 0 + -3 = -3 -1n = -3 Divide each side by '-1'. n = 3 Simplifying n = 3Subproblem 3
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {0, 3, 7}
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