Expand and Simplify 3x(8y-2) - 4y(6x -3) + 2x = 0

1) We will expand the function by multiplying each bracket by its coefficients. Lets divide the equation in two parts to make it a bit simpler: 

          3x(8y-2) = 3x8y + 3x(-2)  = 24xy - 6x                                       

          -4y(6x - 3) + 2x = -4y6x + (-4y)(-3) +2x = -24xy + 12y+ 2x       

A common mistake is to forget to multiply the minus signs, always include the sign when multiplying numbers!

2) Now that we have expanded both sides, we can put them back together:

          24xy - 6x -24xy + 12y + 2x = 0

3) Next step is to gather all the numbers which have the same variables ( x , y or xy)  and add them.

          24xy -24xy - 6x + 2x + 12y = 0 - 4x + 12y = - 4x + 12y = 12y - 4x = 0

          Note that 24xy - 24xy will always equal 0. It is also important to be aware that we can only add the                        numbers which are multiplying the same coefficients.

4) Finally, we can simplify further the final equation 12y -4x by extracting the common factor 4 and obtain:

          12y -4x = 3(4y -x)