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

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

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

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

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

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

Solving
-3 + 2a = 3

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 = 3 + 3

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

Combine like terms: 3 + 3 = 6
2a = 6

Divide each side by '2'.
a = 3

Simplifying
a = 3