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

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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

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