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Simplifying (ax + b)(cx + d) = 1 Multiply (ax + b) * (cx + d) (ax(cx + d) + b(cx + d)) = 1 ((cx * ax + d * ax) + b(cx + d)) = 1 ((acx2 + adx) + b(cx + d)) = 1 (acx2 + adx + (cx * b + d * b)) = 1 (acx2 + adx + (bcx + bd)) = 1 (acx2 + adx + bcx + bd) = 1 Solving acx2 + adx + bcx + bd = 1 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bcx' to each side of the equation. acx2 + adx + bcx + -1bcx + bd = 1 + -1bcx Combine like terms: bcx + -1bcx = 0 acx2 + adx + 0 + bd = 1 + -1bcx acx2 + adx + bd = 1 + -1bcx Add '-1bd' to each side of the equation. acx2 + adx + bd + -1bd = 1 + -1bcx + -1bd Combine like terms: bd + -1bd = 0 acx2 + adx + 0 = 1 + -1bcx + -1bd acx2 + adx = 1 + -1bcx + -1bd Reorder the terms: -1 + acx2 + adx + bcx + bd = 1 + -1bcx + -1bd + -1 + bcx + bd Reorder the terms: -1 + acx2 + adx + bcx + bd = 1 + -1 + -1bcx + bcx + -1bd + bd Combine like terms: 1 + -1 = 0 -1 + acx2 + adx + bcx + bd = 0 + -1bcx + bcx + -1bd + bd -1 + acx2 + adx + bcx + bd = -1bcx + bcx + -1bd + bd Combine like terms: -1bcx + bcx = 0 -1 + acx2 + adx + bcx + bd = 0 + -1bd + bd -1 + acx2 + adx + bcx + bd = -1bd + bd Combine like terms: -1bd + bd = 0 -1 + acx2 + adx + bcx + bd = 0 The solution to this equation could not be determined.
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