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Simplifying (by + d) * x = ay + b Reorder the terms for easier multiplication: x(by + d) = ay + b (by * x + d * x) = ay + b (bxy + dx) = ay + b Solving bxy + dx = ay + b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1b' to each side of the equation. bxy + -1b + dx = ay + b + -1b Reorder the terms: -1b + bxy + dx = ay + b + -1b Combine like terms: b + -1b = 0 -1b + bxy + dx = ay + 0 -1b + bxy + dx = ay Add '-1dx' to each side of the equation. -1b + bxy + dx + -1dx = ay + -1dx Combine like terms: dx + -1dx = 0 -1b + bxy + 0 = ay + -1dx -1b + bxy = ay + -1dx Reorder the terms: -1ay + -1b + bxy + dx = ay + -1dx + -1ay + dx Reorder the terms: -1ay + -1b + bxy + dx = ay + -1ay + -1dx + dx Combine like terms: ay + -1ay = 0 -1ay + -1b + bxy + dx = 0 + -1dx + dx -1ay + -1b + bxy + dx = -1dx + dx Combine like terms: -1dx + dx = 0 -1ay + -1b + bxy + dx = 0 The solution to this equation could not be determined.
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