To solve this, first, expand the terms in parenthesis paying close attention to the signs inside and outside the parenthesis:
#-15p - (5*2) + (5*4p) = (3*p) - (3*2) - 10#
#-15p - 10 + 20p = 3p - 6 - 10#
Now we are able to group and combine like terms on each side of the equation:
#-15p + 20p - 10 = 3p - 16#
#(-15 + 20)p - 10 = 3p - 16#
#5p - 10 = 3p - 16#
Next, we can isolate the #p# terms on one side of the equation and the constants on the other while maintaining the balance of the equation:
#5p - 10 color(red)( + 10 - 3p) = 3p - 16color(red)( + 10 - 3p)#
5p - 0 - 3p = 0 - 16 + 10#
#5p - 3p = -16 + 10#
#(5 - 3)p = -6#
#2p = -6#
Finally, to complete the solution we can solve for #p# while keeping the equation balanced:
#(2p)/color(red)(2) = -6/color(red)(2)#
#(color(red)(cancel(color(black)(2)))p)/color(red)(cancel(color(black)(2))) = -3#
#p = -3#
To check this solution we must substitute #-3# for every occurrence of #p# in the original equation and calculate the results:
#-15p - 5(2 - 4p) = 3(p - 2) - 10#
#(-15*-3) - 5(2 - (4*-3)) = 3(-3 - 2) - 10#
#45 - 5(2 - -12) = (3*-5) - 10#
#45 - 5(2 + 12) = -15 - 10#
#45 - 5(14) = -25#
#45 - 70 = -25#
#-25 = -25#
