x(a+b)-3-a(a-2)=2(x-1)-x(a-b)

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Solution for x(a+b)-3-a(a-2)=2(x-1)-x(a-b) equation:


Simplifying
x(a + b) + -3 + -1a(a + -2) = 2(x + -1) + -1x(a + -1b)
(a * x + b * x) + -3 + -1a(a + -2) = 2(x + -1) + -1x(a + -1b)
(ax + bx) + -3 + -1a(a + -2) = 2(x + -1) + -1x(a + -1b)

Reorder the terms:
ax + bx + -3 + -1a(-2 + a) = 2(x + -1) + -1x(a + -1b)
ax + bx + -3 + (-2 * -1a + a * -1a) = 2(x + -1) + -1x(a + -1b)
ax + bx + -3 + (2a + -1a2) = 2(x + -1) + -1x(a + -1b)

Reorder the terms:
-3 + 2a + ax + -1a2 + bx = 2(x + -1) + -1x(a + -1b)

Reorder the terms:
-3 + 2a + ax + -1a2 + bx = 2(-1 + x) + -1x(a + -1b)
-3 + 2a + ax + -1a2 + bx = (-1 * 2 + x * 2) + -1x(a + -1b)
-3 + 2a + ax + -1a2 + bx = (-2 + 2x) + -1x(a + -1b)
-3 + 2a + ax + -1a2 + bx = -2 + 2x + (a * -1x + -1b * -1x)
-3 + 2a + ax + -1a2 + bx = -2 + 2x + (-1ax + 1bx)

Reorder the terms:
-3 + 2a + ax + -1a2 + bx = -2 + -1ax + 1bx + 2x

Solving
-3 + 2a + ax + -1a2 + bx = -2 + -1ax + 1bx + 2x

Solving for variable 'a'.

Reorder the terms:
-3 + 2 + 2a + ax + ax + -1a2 + bx + -1bx + -2x = -2 + -1ax + 1bx + 2x + 2 + ax + -1bx + -2x

Combine like terms: -3 + 2 = -1
-1 + 2a + ax + ax + -1a2 + bx + -1bx + -2x = -2 + -1ax + 1bx + 2x + 2 + ax + -1bx + -2x

Combine like terms: ax + ax = 2ax
-1 + 2a + 2ax + -1a2 + bx + -1bx + -2x = -2 + -1ax + 1bx + 2x + 2 + ax + -1bx + -2x

Combine like terms: bx + -1bx = 0
-1 + 2a + 2ax + -1a2 + 0 + -2x = -2 + -1ax + 1bx + 2x + 2 + ax + -1bx + -2x
-1 + 2a + 2ax + -1a2 + -2x = -2 + -1ax + 1bx + 2x + 2 + ax + -1bx + -2x

Reorder the terms:
-1 + 2a + 2ax + -1a2 + -2x = -2 + 2 + -1ax + ax + 1bx + -1bx + 2x + -2x

Combine like terms: -2 + 2 = 0
-1 + 2a + 2ax + -1a2 + -2x = 0 + -1ax + ax + 1bx + -1bx + 2x + -2x
-1 + 2a + 2ax + -1a2 + -2x = -1ax + ax + 1bx + -1bx + 2x + -2x

Combine like terms: -1ax + ax = 0
-1 + 2a + 2ax + -1a2 + -2x = 0 + 1bx + -1bx + 2x + -2x
-1 + 2a + 2ax + -1a2 + -2x = 1bx + -1bx + 2x + -2x

Combine like terms: 1bx + -1bx = 0
-1 + 2a + 2ax + -1a2 + -2x = 0 + 2x + -2x
-1 + 2a + 2ax + -1a2 + -2x = 2x + -2x

Combine like terms: 2x + -2x = 0
-1 + 2a + 2ax + -1a2 + -2x = 0

The solution to this equation could not be determined.

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