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Simplifying A(x + b) = c(x + d) Reorder the terms: A(b + x) = c(x + d) (b * A + x * A) = c(x + d) (bA + xA) = c(x + d) Reorder the terms: bA + xA = c(d + x) bA + xA = (d * c + x * c) bA + xA = (cd + cx) Solving bA + xA = cd + cx Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1xA' to each side of the equation. bA + xA + -1xA = cd + cx + -1xA Combine like terms: xA + -1xA = 0 bA + 0 = cd + cx + -1xA bA = cd + cx + -1xA Divide each side by 'A'. b = cdA-1 + cxA-1 + -1x Simplifying b = cdA-1 + cxA-1 + -1x
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