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Simplifying 10n2 + 6n = 28 Reorder the terms: 6n + 10n2 = 28 Solving 6n + 10n2 = 28 Solving for variable 'n'. Reorder the terms: -28 + 6n + 10n2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 6n + 10n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + 3n + 5n2) = 0 Factor a trinomial. 2((-2 + -1n)(7 + -5n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 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 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2Subproblem 2
Set the factor '(7 + -5n)' equal to zero and attempt to solve: Simplifying 7 + -5n = 0 Solving 7 + -5n = 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 + -5n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5n = 0 + -7 -5n = 0 + -7 Combine like terms: 0 + -7 = -7 -5n = -7 Divide each side by '-5'. n = 1.4 Simplifying n = 1.4Solution
n = {-2, 1.4}
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