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Simplifying (a + b)(c + d) + a + b + c + d = -5 Multiply (a + b) * (c + d) (a(c + d) + b(c + d)) + a + b + c + d = -5 ((c * a + d * a) + b(c + d)) + a + b + c + d = -5 ((ac + ad) + b(c + d)) + a + b + c + d = -5 (ac + ad + (c * b + d * b)) + a + b + c + d = -5 (ac + ad + (bc + bd)) + a + b + c + d = -5 (ac + ad + bc + bd) + a + b + c + d = -5 Reorder the terms: a + ac + ad + b + bc + bd + c + d = -5 Solving a + ac + ad + b + bc + bd + c + d = -5 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + ac + ad + b + bc + bd + c + -1b + d = -5 + -1b Reorder the terms: a + ac + ad + b + -1b + bc + bd + c + d = -5 + -1b Combine like terms: b + -1b = 0 a + ac + ad + 0 + bc + bd + c + d = -5 + -1b a + ac + ad + bc + bd + c + d = -5 + -1b Add '-1bc' to each side of the equation. a + ac + ad + bc + bd + c + -1bc + d = -5 + -1b + -1bc Reorder the terms: a + ac + ad + bc + -1bc + bd + c + d = -5 + -1b + -1bc Combine like terms: bc + -1bc = 0 a + ac + ad + 0 + bd + c + d = -5 + -1b + -1bc a + ac + ad + bd + c + d = -5 + -1b + -1bc Add '-1bd' to each side of the equation. a + ac + ad + bd + c + -1bd + d = -5 + -1b + -1bc + -1bd Reorder the terms: a + ac + ad + bd + -1bd + c + d = -5 + -1b + -1bc + -1bd Combine like terms: bd + -1bd = 0 a + ac + ad + 0 + c + d = -5 + -1b + -1bc + -1bd a + ac + ad + c + d = -5 + -1b + -1bc + -1bd Add '-1c' to each side of the equation. a + ac + ad + c + -1c + d = -5 + -1b + -1bc + -1bd + -1c Combine like terms: c + -1c = 0 a + ac + ad + 0 + d = -5 + -1b + -1bc + -1bd + -1c a + ac + ad + d = -5 + -1b + -1bc + -1bd + -1c Add '-1d' to each side of the equation. a + ac + ad + d + -1d = -5 + -1b + -1bc + -1bd + -1c + -1d Combine like terms: d + -1d = 0 a + ac + ad + 0 = -5 + -1b + -1bc + -1bd + -1c + -1d a + ac + ad = -5 + -1b + -1bc + -1bd + -1c + -1d Reorder the terms: 5 + a + ac + ad + b + bc + bd + c + d = -5 + -1b + -1bc + -1bd + -1c + -1d + 5 + b + bc + bd + c + d Reorder the terms: 5 + a + ac + ad + b + bc + bd + c + d = -5 + 5 + -1b + b + -1bc + bc + -1bd + bd + -1c + c + -1d + d Combine like terms: -5 + 5 = 0 5 + a + ac + ad + b + bc + bd + c + d = 0 + -1b + b + -1bc + bc + -1bd + bd + -1c + c + -1d + d 5 + a + ac + ad + b + bc + bd + c + d = -1b + b + -1bc + bc + -1bd + bd + -1c + c + -1d + d Combine like terms: -1b + b = 0 5 + a + ac + ad + b + bc + bd + c + d = 0 + -1bc + bc + -1bd + bd + -1c + c + -1d + d 5 + a + ac + ad + b + bc + bd + c + d = -1bc + bc + -1bd + bd + -1c + c + -1d + d Combine like terms: -1bc + bc = 0 5 + a + ac + ad + b + bc + bd + c + d = 0 + -1bd + bd + -1c + c + -1d + d 5 + a + ac + ad + b + bc + bd + c + d = -1bd + bd + -1c + c + -1d + d Combine like terms: -1bd + bd = 0 5 + a + ac + ad + b + bc + bd + c + d = 0 + -1c + c + -1d + d 5 + a + ac + ad + b + bc + bd + c + d = -1c + c + -1d + d Combine like terms: -1c + c = 0 5 + a + ac + ad + b + bc + bd + c + d = 0 + -1d + d 5 + a + ac + ad + b + bc + bd + c + d = -1d + d Combine like terms: -1d + d = 0 5 + a + ac + ad + b + bc + bd + c + d = 0 The solution to this equation could not be determined.
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