how to factor and solve for x for fx 3x312x23x so you can so

how to factor and solve for x for f(x)= 3x^3-12x^2+3x so you can solve and factor for x without a calculator?

I started out by doing 3x(x^2-4x+1) I just dont know what to do next in regards to the part in the parentheses.

Solution:

Here;

f(x)= 3x^3-12x^2+3x

=> 3x(x^2-4x+1)

Adding 4-4 i.e nothing to make the formula of (a+b)^2

=> 3x(x^2-4x+4 -4 +1)

=> 3x((x-2)²-3)

Now solving for \'x\' :-

=> 3x((x-2)²-3) = 0

=> 3x = 0 and (x-2)²-3 = 0

=> x = 0 and (x-2)² = 3

=> x = 0 and x-2 = ±3

=> x = 0 and x = ±3 + 2

i.e;

x = 0 , x = -3 + 2 , x = 3 + 2