solve for p ?

3/8 (P-4) - 1/2 (3p + 2)= 1/4 (9p-7)

LCM of the denominators

LCM(8,2,4) = 8

Multiply through by 8 (clearing out the denominators)

3(p-4) - 4(3p+2) = 2(9p-7)

3p - 12 - 12p - 8 = 18p - 14

3p - 12p - 18p = 12 + 8 - 14

-27p = 6

p = -6/27 = -2/9

3(p - 4)/8 - 1(3p + 2)/2 = 1(9p - 7)/4
(3p - 12)/8 - (3p + 2)/2 = (9p - 7)/4
8[(3p - 12)/8 - (3p + 2)/2] = 8[(9p - 7)/4]
3p - 12 - 4(3p + 2) = 2(9p - 7)
3p - 12 - 12p - 8 = 18p - 14
3p - 12p - 18p = 12 - 14 + 8
-27p = 6
p = 6/-27
p = -2/9

multiply by 8:
3(p - 4) - 4(3p+2) = 2(9p - 7)
3p - 12 - 12p - 8 = 18p - 14
-9p - 20 = 18p - 14
-27p = 6
p = -6/27 = -2/9

3p - 12 - 12p - 8 = 18p - 14
- 27 p = 6
p = - 2 / 9

3/8 (P-4) - 1/2 (3p + 2)= 1/4 (9p-7)

Let's start this by multiplying everything by 8 to remove the fractions:

3(P - 4) - 4(3p + 2) = 2(9p - 7)

Now we'll simplify the expressions, and move all the p's to one side and the P and the constants to the other:

3P - 12 - 12p - 8 = 18p - 14
3P - 6 = 6p
(3P - 6) / 6 = p

or

(P/2) - 1 = p