Solve y=lim(x^2+1)+3x^2+3x

$$y = \lim ( x ^ { 2 } + 1 ) + 3 x ^ { 2 } + 3 x$$

Solve for l

$$\left\{\begin{matrix}l=-\frac{3x^{2}+3x-y}{Im(x^{2})}\text{, }&Im(x^{2})\neq 0\\l\in \mathrm{C}\text{, }&y=3x\left(x+1\right)\text{ and }Im(x^{2})=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$lIm(x^{2}+1)+3x^{2}+3x=y$$

Subtract 3x^{2} from both sides.

$$lIm(x^{2}+1)+3x=y-3x^{2}$$

Subtract 3x from both sides.

$$lIm(x^{2}+1)=y-3x^{2}-3x$$

The equation is in standard form.

$$Im(x^{2})l=y-3x-3x^{2}$$

Divide both sides by Im(x^{2}).

$$\frac{Im(x^{2})l}{Im(x^{2})}=\frac{y-3x-3x^{2}}{Im(x^{2})}$$

Dividing by Im(x^{2}) undoes the multiplication by Im(x^{2}).

$$l=\frac{y-3x-3x^{2}}{Im(x^{2})}$$