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Simplifying (bx + -1cy) * dy + (ax + -1by) * dx = 0 Reorder the terms for easier multiplication: dy(bx + -1cy) + (ax + -1by) * dx = 0 (bx * dy + -1cy * dy) + (ax + -1by) * dx = 0 (bdxy + -1cdy2) + (ax + -1by) * dx = 0 Reorder the terms for easier multiplication: bdxy + -1cdy2 + dx(ax + -1by) = 0 bdxy + -1cdy2 + (ax * dx + -1by * dx) = 0 bdxy + -1cdy2 + (adx2 + -1bdxy) = 0 Reorder the terms: adx2 + bdxy + -1bdxy + -1cdy2 = 0 Combine like terms: bdxy + -1bdxy = 0 adx2 + 0 + -1cdy2 = 0 adx2 + -1cdy2 = 0 Solving adx2 + -1cdy2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add 'cdy2' to each side of the equation. adx2 + -1cdy2 + cdy2 = 0 + cdy2 Combine like terms: -1cdy2 + cdy2 = 0 adx2 + 0 = 0 + cdy2 adx2 = 0 + cdy2 Remove the zero: adx2 = cdy2 Divide each side by 'dx2'. a = cx-2y2 Simplifying a = cx-2y2
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