2[p-(2p+6)+3]=2(p+3)

Solution for 2[p-(2p+6)+3]=2(p+3) equation:

Simplifying
2[p + -1(2p + 6) + 3] = 2(p + 3)

Reorder the terms:
2[p + -1(6 + 2p) + 3] = 2(p + 3)
2[p + (6 * -1 + 2p * -1) + 3] = 2(p + 3)
2[p + (-6 + -2p) + 3] = 2(p + 3)

Reorder the terms:
2[-6 + 3 + p + -2p] = 2(p + 3)

Combine like terms: -6 + 3 = -3
2[-3 + p + -2p] = 2(p + 3)

Combine like terms: p + -2p = -1p
2[-3 + -1p] = 2(p + 3)
[-3 * 2 + -1p * 2] = 2(p + 3)
[-6 + -2p] = 2(p + 3)

Reorder the terms:
-6 + -2p = 2(3 + p)
-6 + -2p = (3 * 2 + p * 2)
-6 + -2p = (6 + 2p)

Solving
-6 + -2p = 6 + 2p

Solving for variable 'p'.

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

Add '-2p' to each side of the equation.
-6 + -2p + -2p = 6 + 2p + -2p

Combine like terms: -2p + -2p = -4p
-6 + -4p = 6 + 2p + -2p

Combine like terms: 2p + -2p = 0
-6 + -4p = 6 + 0
-6 + -4p = 6

Add '6' to each side of the equation.
-6 + 6 + -4p = 6 + 6

Combine like terms: -6 + 6 = 0
0 + -4p = 6 + 6
-4p = 6 + 6

Combine like terms: 6 + 6 = 12
-4p = 12

Divide each side by '-4'.
p = -3

Simplifying
p = -3