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Simplifying -4n(n + 3) + 3(8n + -5) = 0 Reorder the terms: -4n(3 + n) + 3(8n + -5) = 0 (3 * -4n + n * -4n) + 3(8n + -5) = 0 (-12n + -4n2) + 3(8n + -5) = 0 Reorder the terms: -12n + -4n2 + 3(-5 + 8n) = 0 -12n + -4n2 + (-5 * 3 + 8n * 3) = 0 -12n + -4n2 + (-15 + 24n) = 0 Reorder the terms: -15 + -12n + 24n + -4n2 = 0 Combine like terms: -12n + 24n = 12n -15 + 12n + -4n2 = 0 Solving -15 + 12n + -4n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 3.75 + -3n + n2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -3n + -3.75 + n2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -3n + n2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -3n + n2 = 0 + -3.75 -3n + n2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -3n + n2 = -3.75 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = -3.75 + 2.25 Reorder the terms: 2.25 + -3n + n2 = -3.75 + 2.25 Combine like terms: -3.75 + 2.25 = -1.5 2.25 + -3n + n2 = -1.5 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = -1.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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