Hold up. Hee haw. Whoa! Your first instinct was to multiply it out and get rid of the parentheses. That's often a good instinct, but this time, it made things harder for you.
This is a good example of a rule you should consider:
Before you do anything to anything, sit back, relax, LOOK at the problem, THINK about it, and plan your strategy. Decide what the solution might look like, and what you're going to do to the given information in order to move towards the solution.
You might look at this particular equation and ponder:
-- If I multiplied this thing out and got rid of the parentheses, it would have x³ in it. So there are going to be 3 solutions.
-- If either factor is zero, then the equation is true.
-- One of the factors is 6x. Setting that to zero gives one solution: x=0.
-- The other two solutions come from setting (4x² - 4) = 0 .
-- That's the difference of 2 squares, so it's (2x + 2) (2x - 2) = 0
-- The other 2 solutions come from setting each of those factors to zero.
There you are. You got this far just by thinking, without even picking up your pencil yet.
6x( 4x^2 -4) = 0 then 6x = 0 --- eqn.1 or (4x^2-4) = 0 --- eqn.2 from eqn.1 we get that x=0 from eqn.2 we get: 4x^2=4 x^2=1 x^2 - 1 =0 (x-1) * (x+1) = 0 so x = +1 and -1 the final answer is x= 0, -1 , 1
