AX+B+(-1XB)=C

Solution for AX+B+(-1XB)=C equation:

Simplifying
AX + B + (-1XB) = C

Solving
AX + B + (-1BX) = C

Solving for variable 'A'.

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

Add '-1B' to each side of the equation.
AX + B + -1B + (-1BX) = -1B + C

Combine like terms: B + -1B = 0
AX + 0 + (-1BX) = -1B + C
AX + (-1BX) = -1B + C

Add '(BX)' to each side of the equation.
AX + (-1BX) + (BX) = -1B + (BX) + C
AX + (-1BX) + BX = -1B + (BX) + C

Combine like terms: (-1BX) + BX = 0
AX + 0 = -1B + (BX) + C
AX = -1B + (BX) + C
AX = -1B + BX + C

Divide each side by 'X'.
A = -1BX-1 + B + CX-1

Simplifying
A = -1BX-1 + B + CX-1

Reorder the terms:
A = B + -1BX-1 + CX-1