a(x+a)-x=a(a+1)+1

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

Simplifying
a(x + a) + -1x = a(a + 1) + 1

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

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

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

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

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

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

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

Solving
ax + -1x = 1 + 1a

Solving for variable 'a'.

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.