Question

(-6x^3+2x^2-2x)/(2x-1) how do I solve using long division?

Answer 1

Check  the picture below.

the idea being, to cancel out the leftmost term in the dividend, you multiply the leftmost term in the divisor, by something that will "mimic" or equate the leftmost term in the dividend, and then you slap the negative -( ) to the expression, and poof it goes.

Answer 2

$(-6x^3+2x^2-2x):(2x-1)=-3x^2-\dfrac{1}{2}x-1\dfrac{1}{4}\ R=-1\dfrac{1}{4}\\\\-6x^3+2x^2-2x=\left(-3x^2-\dfrac{1}{2}x-1\dfrac{1}{4}\right)(2x-1)-1\dfrac{1}{4}$