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

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

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

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

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

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

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

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

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

Reorder the terms:
2 = (3 + a)

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

Solving
2 = 3 + a

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.
2 + -1a = 3 + a + -1a

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

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

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

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

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

Simplifying
a = -1