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 = 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 = -2
2a = -2

Divide each side by '2'.
a = -1

Simplifying
a = -1