One root of f(x) = 2x³ + 9x² + 7x – 6 is –3 this means
(x+3) is a factor of polynomial.

So, to find we will try to reduce this cubic into a quadratic equation by using this given factor.

To do that we have to take out x+3 common out from the equation
f(x) = 2x³ + 9x² + 7x – 6

Splitting the x² and x term and getting x+3 common
=> 2x³ + 6 x² + 3 x² + 9x – 2x – 6

=> 2x² .( x + 3) + 3x .(x + 3) -2 .(x +3)

=> ( x+3) .( 2x^2 + 3x -2 )

Now factorizing the quadratic equation as usual.
=> (x +3) ( 2 x² + 4x – x – 2)

=> ( x +3) [ 2x (x + 2) – ( x+ 2)]

=> ( x + 3 )( x + 2) ( 2x – 1 ) = 0

x + 2 = 0 or 2x – 1 = 0

So, the other factors are -2 and 1/2

Note: If you are not able to take the given factor common as shown above, you can also use polynomial division to get the quadratic.