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

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

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

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

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

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

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

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

Solving for variable 'a'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Add 'bx' to each side of the equation.
-1a + -1ax + -1bx + bx = 3b + 2bx + bx

Combine like terms: -1bx + bx = 0
-1a + -1ax + 0 = 3b + 2bx + bx
-1a + -1ax = 3b + 2bx + bx

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

Reorder the terms:
-1a + -1ax + -3b + -3bx = 3b + -3b + 3bx + -3bx

Combine like terms: 3b + -3b = 0
-1a + -1ax + -3b + -3bx = 0 + 3bx + -3bx
-1a + -1ax + -3b + -3bx = 3bx + -3bx

Combine like terms: 3bx + -3bx = 0
-1a + -1ax + -3b + -3bx = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(a + ax + 3b + 3bx) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(a + ax + 3b + 3bx)' equal to zero and attempt to solve:

Simplifying
a + ax + 3b + 3bx = 0

Solving
a + ax + 3b + 3bx = 0

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

Add '-3b' to each side of the equation.
a + ax + 3b + -3b + 3bx = 0 + -3b

Combine like terms: 3b + -3b = 0
a + ax + 0 + 3bx = 0 + -3b
a + ax + 3bx = 0 + -3b
Remove the zero:
a + ax + 3bx = -3b

Add '-3bx' to each side of the equation.
a + ax + 3bx + -3bx = -3b + -3bx

Combine like terms: 3bx + -3bx = 0
a + ax + 0 = -3b + -3bx
a + ax = -3b + -3bx

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.