a+(a-3)=a+2-(a+1)

Solution for a+(a-3)=a+2-(a+1) equation:

Simplifying
a + (a + -3) = a + 2 + -1(a + 1)

Reorder the terms:
a + (-3 + a) = a + 2 + -1(a + 1)

Remove parenthesis around (-3 + a)
a + -3 + a = a + 2 + -1(a + 1)

Reorder the terms:
-3 + a + a = a + 2 + -1(a + 1)

Combine like terms: a + a = 2a
-3 + 2a = a + 2 + -1(a + 1)

Reorder the terms:
-3 + 2a = a + 2 + -1(1 + a)
-3 + 2a = a + 2 + (1 * -1 + a * -1)
-3 + 2a = a + 2 + (-1 + -1a)

Reorder the terms:
-3 + 2a = 2 + -1 + a + -1a

Combine like terms: 2 + -1 = 1
-3 + 2a = 1 + a + -1a

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

Solving
-3 + 2a = 1

Solving for variable 'a'.

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

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

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

Combine like terms: 1 + 3 = 4
2a = 4

Divide each side by '2'.
a = 2

Simplifying
a = 2