Solve left(m+1right)x^2+3x+3=0

$$\left( m+1 \right) { x }^{ 2 } +3x+3=0$$

Solve for m

$$m=-1-\frac{3}{x}-\frac{3}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply m+1 by x^{2}.

$$mx^{2}+x^{2}+3x+3=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$mx^{2}+3x+3=-x^{2}$$

Subtract 3x from both sides.

$$mx^{2}+3=-x^{2}-3x$$

Subtract 3 from both sides.

$$mx^{2}=-x^{2}-3x-3$$

The equation is in standard form.

$$x^{2}m=-x^{2}-3x-3$$

Divide both sides by x^{2}.

$$\frac{x^{2}m}{x^{2}}=\frac{-x^{2}-3x-3}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$m=\frac{-x^{2}-3x-3}{x^{2}}$$

Divide -x^{2}-3x-3 by x^{2}.

$$m=-1-\frac{3x+3}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{3\left(-4m-1\right)}-3}{2\left(m+1\right)}\text{; }x=-\frac{\sqrt{3}\left(\sqrt{-4m-1}+\sqrt{3}\right)}{2\left(m+1\right)}\text{, }&m\neq -1\\x=-1\text{, }&m=-1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{3\left(-4m-1\right)}-3}{2\left(m+1\right)}\text{; }x=-\frac{\sqrt{3}\left(\sqrt{-4m-1}+\sqrt{3}\right)}{2\left(m+1\right)}\text{, }&m\neq -1\text{ and }m\leq -\frac{1}{4}\\x=-1\text{, }&m=-1\end{matrix}\right.$$