to #1)

multiply the equation by 6:

...... Expand the brackets, collect like terms, separate x at the LHS, constants to the RHS, I've got x = 5

to #2)

I assume that you mean

...... Muliply by (3x+1), expand the bracket at the RHS, I've got

to #3)

multiply by x, collect the x at the RHS, divide by the coefficient of x (by the way, it's (-1)), I've got x = 1

to #4)

expand the brackets, collect like terms, solve the quadratic for x:

...... A product equals zero if one factor equals zero. Thus:

to #5

there is nothing to solve because this is only a term. (I assume that there is a typo)

to #6)