First, multiply each side of the equation by the lowest common denominator of the two fractions which is color(red)(40) to eliminate the fractions while keeping the equation balanced:
color(red)(40) xx (p - 2)/5 = color(red)(40) xx p/8
cancel(color(red)(40))8 xx (p - 2)/color(red)(cancel(color(black)(5))) = cancel(color(red)(40))5 xx p/color(red)(cancel(color(black)(8)))
8(p - 2) = 5p
Next, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:
color(red)(8)(p - 2) = 5p
(color(red)(8) xx p) - (color(red)(8) xx 2) = 5p
8p - 16 = 5p
Then, add color(red)(16) and subtract color(blue)(5p) from each side of the equation to isolate the p term while keeping the equation balanced:
-color(blue)(5p) + 8p - 16 + color(red)(16) = -color(blue)(5p) + 5p + color(red)(16)
(-color(blue)(5) + 8)p - 0 = 0 + 16
3p = 16
Now, divide each side of the equation by color(red)(3) to solve for p while keeping the equation balanced:
(3p)/color(red)(3) = 16/color(red)(3)
(color(red)(cancel(color(black)(3)))p)/cancel(color(red)(3)) = 16/3
p = 16/3