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Simplifying (a + b)(c + d)(e + f) = 0 Multiply (a + b) * (c + d) (a(c + d) + b(c + d))(e + f) = 0 ((c * a + d * a) + b(c + d))(e + f) = 0 ((ac + ad) + b(c + d))(e + f) = 0 (ac + ad + (c * b + d * b))(e + f) = 0 (ac + ad + (bc + bd))(e + f) = 0 (ac + ad + bc + bd)(e + f) = 0 Multiply (ac + ad + bc + bd) * (e + f) (ac(e + f) + ad(e + f) + bc(e + f) + bd(e + f)) = 0 ((e * ac + f * ac) + ad(e + f) + bc(e + f) + bd(e + f)) = 0 ((ace + acf) + ad(e + f) + bc(e + f) + bd(e + f)) = 0 (ace + acf + (e * ad + f * ad) + bc(e + f) + bd(e + f)) = 0 (ace + acf + (ade + adf) + bc(e + f) + bd(e + f)) = 0 (ace + acf + ade + adf + (e * bc + f * bc) + bd(e + f)) = 0 (ace + acf + ade + adf + (bce + bcf) + bd(e + f)) = 0 (ace + acf + ade + adf + bce + bcf + (e * bd + f * bd)) = 0 (ace + acf + ade + adf + bce + bcf + (bde + bdf)) = 0 (ace + acf + ade + adf + bce + bcf + bde + bdf) = 0 Solving ace + acf + ade + adf + bce + bcf + bde + bdf = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bce' to each side of the equation. ace + acf + ade + adf + bce + bcf + bde + -1bce + bdf = 0 + -1bce Reorder the terms: ace + acf + ade + adf + bce + -1bce + bcf + bde + bdf = 0 + -1bce Combine like terms: bce + -1bce = 0 ace + acf + ade + adf + 0 + bcf + bde + bdf = 0 + -1bce ace + acf + ade + adf + bcf + bde + bdf = 0 + -1bce Remove the zero: ace + acf + ade + adf + bcf + bde + bdf = -1bce Add '-1bcf' to each side of the equation. ace + acf + ade + adf + bcf + bde + -1bcf + bdf = -1bce + -1bcf Reorder the terms: ace + acf + ade + adf + bcf + -1bcf + bde + bdf = -1bce + -1bcf Combine like terms: bcf + -1bcf = 0 ace + acf + ade + adf + 0 + bde + bdf = -1bce + -1bcf ace + acf + ade + adf + bde + bdf = -1bce + -1bcf Add '-1bde' to each side of the equation. ace + acf + ade + adf + bde + -1bde + bdf = -1bce + -1bcf + -1bde Combine like terms: bde + -1bde = 0 ace + acf + ade + adf + 0 + bdf = -1bce + -1bcf + -1bde ace + acf + ade + adf + bdf = -1bce + -1bcf + -1bde Add '-1bdf' to each side of the equation. ace + acf + ade + adf + bdf + -1bdf = -1bce + -1bcf + -1bde + -1bdf Combine like terms: bdf + -1bdf = 0 ace + acf + ade + adf + 0 = -1bce + -1bcf + -1bde + -1bdf ace + acf + ade + adf = -1bce + -1bcf + -1bde + -1bdf Reorder the terms: ace + acf + ade + adf + bce + bcf + bde + bdf = -1bce + bce + -1bcf + bcf + -1bde + bde + -1bdf + bdf Combine like terms: -1bce + bce = 0 ace + acf + ade + adf + bce + bcf + bde + bdf = 0 + -1bcf + bcf + -1bde + bde + -1bdf + bdf ace + acf + ade + adf + bce + bcf + bde + bdf = -1bcf + bcf + -1bde + bde + -1bdf + bdf Combine like terms: -1bcf + bcf = 0 ace + acf + ade + adf + bce + bcf + bde + bdf = 0 + -1bde + bde + -1bdf + bdf ace + acf + ade + adf + bce + bcf + bde + bdf = -1bde + bde + -1bdf + bdf Combine like terms: -1bde + bde = 0 ace + acf + ade + adf + bce + bcf + bde + bdf = 0 + -1bdf + bdf ace + acf + ade + adf + bce + bcf + bde + bdf = -1bdf + bdf Combine like terms: -1bdf + bdf = 0 ace + acf + ade + adf + bce + bcf + bde + bdf = 0 The solution to this equation could not be determined.
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