A(2+x)+B(x-1)-1=0

Solution for A(2+x)+B(x-1)-1=0 equation:

Simplifying
A(2 + x) + B(x + -1) + -1 = 0
(2 * A + x * A) + B(x + -1) + -1 = 0
(2A + xA) + B(x + -1) + -1 = 0

Reorder the terms:
2A + xA + B(-1 + x) + -1 = 0
2A + xA + (-1 * B + x * B) + -1 = 0
2A + xA + (-1B + xB) + -1 = 0

Reorder the terms:
-1 + 2A + -1B + xA + xB = 0

Solving
-1 + 2A + -1B + xA + xB = 0

Solving for variable 'A'.

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

Add '1' to each side of the equation.
-1 + 2A + -1B + xA + 1 + xB = 0 + 1

Reorder the terms:
-1 + 1 + 2A + -1B + xA + xB = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2A + -1B + xA + xB = 0 + 1
2A + -1B + xA + xB = 0 + 1

Combine like terms: 0 + 1 = 1
2A + -1B + xA + xB = 1

Add 'B' to each side of the equation.
2A + -1B + xA + B + xB = 1 + B

Reorder the terms:
2A + -1B + B + xA + xB = 1 + B

Combine like terms: -1B + B = 0
2A + 0 + xA + xB = 1 + B
2A + xA + xB = 1 + B

Add '-1xB' to each side of the equation.
2A + xA + xB + -1xB = 1 + B + -1xB

Combine like terms: xB + -1xB = 0
2A + xA + 0 = 1 + B + -1xB
2A + xA = 1 + B + -1xB

Reorder the terms:
-1 + 2A + -1B + xA + xB = 1 + B + -1xB + -1 + -1B + xB

Reorder the terms:
-1 + 2A + -1B + xA + xB = 1 + -1 + B + -1B + -1xB + xB

Combine like terms: 1 + -1 = 0
-1 + 2A + -1B + xA + xB = 0 + B + -1B + -1xB + xB
-1 + 2A + -1B + xA + xB = B + -1B + -1xB + xB

Combine like terms: B + -1B = 0
-1 + 2A + -1B + xA + xB = 0 + -1xB + xB
-1 + 2A + -1B + xA + xB = -1xB + xB

Combine like terms: -1xB + xB = 0
-1 + 2A + -1B + xA + xB = 0

The solution to this equation could not be determined.