ax-a(a+b)=-x-1(1+ab)

Solution for ax-a(a+b)=-x-1(1+ab) equation:

Simplifying
ax + -1a(a + b) = -1x + -1(1 + ab)
ax + (a * -1a + b * -1a) = -1x + -1(1 + ab)

Reorder the terms:
ax + (-1ab + -1a2) = -1x + -1(1 + ab)
ax + (-1ab + -1a2) = -1x + -1(1 + ab)

Reorder the terms:
-1ab + ax + -1a2 = -1x + -1(1 + ab)
-1ab + ax + -1a2 = -1x + (1 * -1 + ab * -1)
-1ab + ax + -1a2 = -1x + (-1 + -1ab)

Reorder the terms:
-1ab + ax + -1a2 = -1 + -1ab + -1x

Add 'ab' to each side of the equation.
-1ab + ax + ab + -1a2 = -1 + -1ab + ab + -1x

Reorder the terms:
-1ab + ab + ax + -1a2 = -1 + -1ab + ab + -1x

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

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

Solving
ax + -1a2 = -1 + -1x

Solving for variable 'a'.

Reorder the terms:
1 + ax + -1a2 + x = -1 + -1x + 1 + x

Reorder the terms:
1 + ax + -1a2 + x = -1 + 1 + -1x + x

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

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

The solution to this equation could not be determined.