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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
1 + 2a = 3 + 4a

Solving for variable 'a'.

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

Add '-4a' to each side of the equation.
1 + 2a + -4a = 3 + 4a + -4a

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

Combine like terms: 4a + -4a = 0
1 + -2a = 3 + 0
1 + -2a = 3

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

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

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

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

Simplifying
a = -1