A(a+b)-2b(x+a)=x(a+b)

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Solution for A(a+b)-2b(x+a)=x(a+b) equation: 


Simplifying
A(a + b) + -2b(x + a) = x(a + b)
(a * A + b * A) + -2b(x + a) = x(a + b)
(aA + bA) + -2b(x + a) = x(a + b)

Reorder the terms:
aA + bA + -2b(a + x) = x(a + b)
aA + bA + (a * -2b + x * -2b) = x(a + b)
aA + bA + (-2ab + -2bx) = x(a + b)

Reorder the terms:
aA + -2ab + bA + -2bx = x(a + b)
aA + -2ab + bA + -2bx = (a * x + b * x)
aA + -2ab + bA + -2bx = (ax + bx)

Solving
aA + -2ab + bA + -2bx = 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.
aA + -2ab + bA + -1ax + -2bx = ax + -1ax + bx

Reorder the terms:
aA + -2ab + -1ax + bA + -2bx = ax + -1ax + bx

Combine like terms: ax + -1ax = 0
aA + -2ab + -1ax + bA + -2bx = 0 + bx
aA + -2ab + -1ax + bA + -2bx = bx

Add '-1bA' to each side of the equation.
aA + -2ab + -1ax + bA + -1bA + -2bx = -1bA + bx

Combine like terms: bA + -1bA = 0
aA + -2ab + -1ax + 0 + -2bx = -1bA + bx
aA + -2ab + -1ax + -2bx = -1bA + bx

Add '2bx' to each side of the equation.
aA + -2ab + -1ax + -2bx + 2bx = -1bA + bx + 2bx

Combine like terms: -2bx + 2bx = 0
aA + -2ab + -1ax + 0 = -1bA + bx + 2bx
aA + -2ab + -1ax = -1bA + bx + 2bx

Combine like terms: bx + 2bx = 3bx
aA + -2ab + -1ax = -1bA + 3bx

Reorder the terms:
aA + -2ab + -1ax + bA + -3bx = -1bA + bA + 3bx + -3bx

Combine like terms: -1bA + bA = 0
aA + -2ab + -1ax + bA + -3bx = 0 + 3bx + -3bx
aA + -2ab + -1ax + bA + -3bx = 3bx + -3bx

Combine like terms: 3bx + -3bx = 0
aA + -2ab + -1ax + bA + -3bx = 0

The solution to this equation could not be determined.

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