(a-x)(x-2)-(b-x)(x+2)=4(x-b)

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Solution for (a-x)(x-2)-(b-x)(x+2)=4(x-b) equation: 


Simplifying
(a + -1x)(x + -2) + -1(b + -1x)(x + 2) = 4(x + -1b)

Reorder the terms:
(a + -1x)(-2 + x) + -1(b + -1x)(x + 2) = 4(x + -1b)

Multiply (a + -1x) * (-2 + x)
(a(-2 + x) + -1x * (-2 + x)) + -1(b + -1x)(x + 2) = 4(x + -1b)
((-2 * a + x * a) + -1x * (-2 + x)) + -1(b + -1x)(x + 2) = 4(x + -1b)
((-2a + ax) + -1x * (-2 + x)) + -1(b + -1x)(x + 2) = 4(x + -1b)
(-2a + ax + (-2 * -1x + x * -1x)) + -1(b + -1x)(x + 2) = 4(x + -1b)
(-2a + ax + (2x + -1x2)) + -1(b + -1x)(x + 2) = 4(x + -1b)
(-2a + ax + 2x + -1x2) + -1(b + -1x)(x + 2) = 4(x + -1b)

Reorder the terms:
-2a + ax + 2x + -1x2 + -1(b + -1x)(2 + x) = 4(x + -1b)

Multiply (b + -1x) * (2 + x)
-2a + ax + 2x + -1x2 + -1(b(2 + x) + -1x * (2 + x)) = 4(x + -1b)
-2a + ax + 2x + -1x2 + -1((2 * b + x * b) + -1x * (2 + x)) = 4(x + -1b)
-2a + ax + 2x + -1x2 + -1((2b + bx) + -1x * (2 + x)) = 4(x + -1b)
-2a + ax + 2x + -1x2 + -1(2b + bx + (2 * -1x + x * -1x)) = 4(x + -1b)
-2a + ax + 2x + -1x2 + -1(2b + bx + (-2x + -1x2)) = 4(x + -1b)
-2a + ax + 2x + -1x2 + -1(2b + bx + -2x + -1x2) = 4(x + -1b)
-2a + ax + 2x + -1x2 + (2b * -1 + bx * -1 + -2x * -1 + -1x2 * -1) = 4(x + -1b)
-2a + ax + 2x + -1x2 + (-2b + -1bx + 2x + 1x2) = 4(x + -1b)

Reorder the terms:
-2a + ax + -2b + -1bx + 2x + 2x + -1x2 + 1x2 = 4(x + -1b)

Combine like terms: 2x + 2x = 4x
-2a + ax + -2b + -1bx + 4x + -1x2 + 1x2 = 4(x + -1b)

Combine like terms: -1x2 + 1x2 = 0
-2a + ax + -2b + -1bx + 4x + 0 = 4(x + -1b)
-2a + ax + -2b + -1bx + 4x = 4(x + -1b)

Reorder the terms:
-2a + ax + -2b + -1bx + 4x = 4(-1b + x)
-2a + ax + -2b + -1bx + 4x = (-1b * 4 + x * 4)
-2a + ax + -2b + -1bx + 4x = (-4b + 4x)

Add '-4x' to each side of the equation.
-2a + ax + -2b + -1bx + 4x + -4x = -4b + 4x + -4x

Combine like terms: 4x + -4x = 0
-2a + ax + -2b + -1bx + 0 = -4b + 4x + -4x
-2a + ax + -2b + -1bx = -4b + 4x + -4x

Combine like terms: 4x + -4x = 0
-2a + ax + -2b + -1bx = -4b + 0
-2a + ax + -2b + -1bx = -4b

Solving
-2a + ax + -2b + -1bx = -4b

Solving for variable 'a'.

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

Add '2b' to each side of the equation.
-2a + ax + -2b + 2b + -1bx = -4b + 2b

Combine like terms: -2b + 2b = 0
-2a + ax + 0 + -1bx = -4b + 2b
-2a + ax + -1bx = -4b + 2b

Combine like terms: -4b + 2b = -2b
-2a + ax + -1bx = -2b

Add 'bx' to each side of the equation.
-2a + ax + -1bx + bx = -2b + bx

Combine like terms: -1bx + bx = 0
-2a + ax + 0 = -2b + bx
-2a + ax = -2b + bx

Reorder the terms:
-2a + ax + 2b + -1bx = -2b + 2b + bx + -1bx

Combine like terms: -2b + 2b = 0
-2a + ax + 2b + -1bx = 0 + bx + -1bx
-2a + ax + 2b + -1bx = bx + -1bx

Combine like terms: bx + -1bx = 0
-2a + ax + 2b + -1bx = 0

The solution to this equation could not be determined.

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