(a+b)(x+y)=a(X+y)+b(X+y)

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Solution for (a+b)(x+y)=a(X+y)+b(X+y) equation: 


Simplifying
(a + b)(x + y) = a(X + y) + b(X + y)

Multiply (a + b) * (x + y)
(a(x + y) + b(x + y)) = a(X + y) + b(X + y)
((x * a + y * a) + b(x + y)) = a(X + y) + b(X + y)
((ax + ay) + b(x + y)) = a(X + y) + b(X + y)
(ax + ay + (x * b + y * b)) = a(X + y) + b(X + y)
(ax + ay + (bx + by)) = a(X + y) + b(X + y)
(ax + ay + bx + by) = a(X + y) + b(X + y)
ax + ay + bx + by = (X * a + y * a) + b(X + y)
ax + ay + bx + by = (aX + ay) + b(X + y)
ax + ay + bx + by = aX + ay + (X * b + y * b)
ax + ay + bx + by = aX + ay + (bX + by)

Add '-1ay' to each side of the equation.
ax + ay + bx + -1ay + by = aX + ay + bX + -1ay + by

Reorder the terms:
ax + ay + -1ay + bx + by = aX + ay + bX + -1ay + by

Combine like terms: ay + -1ay = 0
ax + 0 + bx + by = aX + ay + bX + -1ay + by
ax + bx + by = aX + ay + bX + -1ay + by

Reorder the terms:
ax + bx + by = aX + ay + -1ay + bX + by

Combine like terms: ay + -1ay = 0
ax + bx + by = aX + 0 + bX + by
ax + bx + by = aX + bX + by

Add '-1by' to each side of the equation.
ax + bx + by + -1by = aX + bX + by + -1by

Combine like terms: by + -1by = 0
ax + bx + 0 = aX + bX + by + -1by
ax + bx = aX + bX + by + -1by

Combine like terms: by + -1by = 0
ax + bx = aX + bX + 0
ax + bx = aX + bX

Solving
ax + bx = aX + bX

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1aX' to each side of the equation.
ax + -1aX + bx = aX + -1aX + bX

Reorder the terms:
-1aX + ax + bx = aX + -1aX + bX

Combine like terms: aX + -1aX = 0
-1aX + ax + bx = 0 + bX
-1aX + ax + bx = bX

Add '-1bx' to each side of the equation.
-1aX + ax + bx + -1bx = bX + -1bx

Combine like terms: bx + -1bx = 0
-1aX + ax + 0 = bX + -1bx
-1aX + ax = bX + -1bx

Reorder the terms:
-1aX + ax + -1bX + bx = bX + -1bX + -1bx + bx

Combine like terms: bX + -1bX = 0
-1aX + ax + -1bX + bx = 0 + -1bx + bx
-1aX + ax + -1bX + bx = -1bx + bx

Combine like terms: -1bx + bx = 0
-1aX + ax + -1bX + bx = 0

The solution to this equation could not be determined.

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