Determine the monotonic intervals of the functions

i need to determine the monotonic intervals of this function $y=2{x}^{3}-6{x}^{2}-18x-7$. I tried the below but i am not sure if i am doing it right.

My work: $\begin{array}{rl}y=2{x}^{3}-6{x}^{2}-18x-7& \u27fa6{x}^{2}-12x-18=0\\ & \u27fa6({x}^{2}-2x-3)=0\\ & \u27fa(x-3)(x+1)\\ & \u27fax-3=0x+1=0\\ & \u27fax=3,x=-1\end{array}$

so my function increases when $x\in [3,+\mathrm{\infty}[$ and decreases when $x\in [-1,3]\cup ]-\mathrm{\infty},-1]$.

Please i want to know how to solve this problem any help with explanation will be appreciated. thanks in advanced

i need to determine the monotonic intervals of this function $y=2{x}^{3}-6{x}^{2}-18x-7$. I tried the below but i am not sure if i am doing it right.

My work: $\begin{array}{rl}y=2{x}^{3}-6{x}^{2}-18x-7& \u27fa6{x}^{2}-12x-18=0\\ & \u27fa6({x}^{2}-2x-3)=0\\ & \u27fa(x-3)(x+1)\\ & \u27fax-3=0x+1=0\\ & \u27fax=3,x=-1\end{array}$

so my function increases when $x\in [3,+\mathrm{\infty}[$ and decreases when $x\in [-1,3]\cup ]-\mathrm{\infty},-1]$.

Please i want to know how to solve this problem any help with explanation will be appreciated. thanks in advanced