Solve 3mx+(m^2+1)y-5=0

$$3 m x + ( m ^ { 2 } + 1 ) y - 5 = 0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{ym^{2}+y-5}{3m}\text{, }&m\neq 0\\x\in \mathrm{C}\text{, }&y=5\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$3mx+m^{2}y+y-5=0$$

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

$$3mx+y-5=-m^{2}y$$

Subtract y from both sides.

$$3mx-5=-m^{2}y-y$$

Add 5 to both sides.

$$3mx=-m^{2}y-y+5$$

Reorder the terms.

$$3mx=-ym^{2}-y+5$$

The equation is in standard form.

$$3mx=5-y-ym^{2}$$

Divide both sides by 3m.

$$\frac{3mx}{3m}=\frac{5-y-ym^{2}}{3m}$$

Dividing by 3m undoes the multiplication by 3m.

$$x=\frac{5-y-ym^{2}}{3m}$$

Divide -ym^{2}-y+5 by 3m.

$$x=-\frac{my}{3}+\frac{5-y}{3m}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{ym^{2}+y-5}{3m}\text{, }&m\neq 0\\x\in \mathrm{R}\text{, }&y=5\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$3mx+m^{2}y+y-5=0$$

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

$$3mx+y-5=-m^{2}y$$

Subtract y from both sides.

$$3mx-5=-m^{2}y-y$$

Add 5 to both sides.

$$3mx=-m^{2}y-y+5$$

Reorder the terms.

$$3mx=-ym^{2}-y+5$$

The equation is in standard form.

$$3mx=5-y-ym^{2}$$

Divide both sides by 3m.

$$\frac{3mx}{3m}=\frac{5-y-ym^{2}}{3m}$$

Dividing by 3m undoes the multiplication by 3m.

$$x=\frac{5-y-ym^{2}}{3m}$$

Divide -ym^{2}-y+5 by 3m.

$$x=-\frac{my}{3}+\frac{5-y}{3m}$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{\sqrt{9x^{2}-4y^{2}+20y}-3x}{2y}\text{; }m=-\frac{\sqrt{9x^{2}-4y^{2}+20y}+3x}{2y}\text{, }&y\neq 0\\m=\frac{5}{3x}\text{, }&y=0\text{ and }x\neq 0\end{matrix}\right.$$

Solve for m

$$\left\{\begin{matrix}m=\frac{\sqrt{9x^{2}-4y^{2}+20y}-3x}{2y}\text{; }m=-\frac{\sqrt{9x^{2}-4y^{2}+20y}+3x}{2y}\text{, }&\left(y>0\text{ and }y<5\right)\text{ or }\left(y\neq 0\text{ and }|x|\geq \frac{2\sqrt{y\left(y-5\right)}}{3}\right)\\m=\frac{5}{3x}\text{, }&y=0\text{ and }x\neq 0\end{matrix}\right.$$