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

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

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

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

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

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

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

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

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

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

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

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

Combine like terms: p + -1p = 0
-2 + 2p = 2 + 0
-2 + 2p = 2

Solving
-2 + 2p = 2

Solving for variable 'p'.

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

Add '2' to each side of the equation.
-2 + 2 + 2p = 2 + 2

Combine like terms: -2 + 2 = 0
0 + 2p = 2 + 2
2p = 2 + 2

Combine like terms: 2 + 2 = 4
2p = 4

Divide each side by '2'.
p = 2

Simplifying
p = 2