2(4-p)-(-3)(p-2)=(2p-1)

Solution for 2(4-p)-(-3)(p-2)=(2p-1) equation:

Simplifying
2(4 + -1p) + -1(-3)(p + -2) = (2p + -1)
(4 * 2 + -1p * 2) + -1(-3)(p + -2) = (2p + -1)
(8 + -2p) + -1(-3)(p + -2) = (2p + -1)

Reorder the terms:
8 + -2p + -1 * -3(-2 + p) = (2p + -1)

Multiply -1 * -3
8 + -2p + 3(-2 + p) = (2p + -1)
8 + -2p + (-2 * 3 + p * 3) = (2p + -1)
8 + -2p + (-6 + 3p) = (2p + -1)

Reorder the terms:
8 + -6 + -2p + 3p = (2p + -1)

Combine like terms: 8 + -6 = 2
2 + -2p + 3p = (2p + -1)

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

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

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

Solving
2 + 1p = -1 + 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.
2 + 1p + -2p = -1 + 2p + -2p

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

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

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

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

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

Divide each side by '-1'.
p = 3

Simplifying
p = 3