Solve 5bx^2-mn=p+4bx^2.text{Despejar:}x

$$5 b x ^ { 2 } - m n = p + 4 b x ^ { 2 } . \text { Despejar: } x$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{mn+p}{x^{2}}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&p=-mn\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4bx^{2} from both sides.

$$5bx^{2}-mn-4bx^{2}=p$$

Combine 5bx^{2} and -4bx^{2} to get bx^{2}.

$$bx^{2}-mn=p$$

Add mn to both sides.

$$bx^{2}=p+mn$$

The equation is in standard form.

$$x^{2}b=mn+p$$

Divide both sides by x^{2}.

$$\frac{x^{2}b}{x^{2}}=\frac{mn+p}{x^{2}}$$

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

$$b=\frac{mn+p}{x^{2}}$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{bx^{2}-p}{n}\text{, }&n\neq 0\\m\in \mathrm{C}\text{, }&p=bx^{2}\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 5bx^{2} from both sides.

$$-mn=p+4bx^{2}-5bx^{2}$$

Combine 4bx^{2} and -5bx^{2} to get -bx^{2}.

$$-mn=p-bx^{2}$$

The equation is in standard form.

$$\left(-n\right)m=p-bx^{2}$$

Divide both sides by -n.

$$\frac{\left(-n\right)m}{-n}=\frac{p-bx^{2}}{-n}$$

Dividing by -n undoes the multiplication by -n.

$$m=\frac{p-bx^{2}}{-n}$$

Divide p-bx^{2} by -n.

$$m=-\frac{p-bx^{2}}{n}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{mn+p}{x^{2}}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&p=-mn\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4bx^{2} from both sides.

$$5bx^{2}-mn-4bx^{2}=p$$

Combine 5bx^{2} and -4bx^{2} to get bx^{2}.

$$bx^{2}-mn=p$$

Add mn to both sides.

$$bx^{2}=p+mn$$

The equation is in standard form.

$$x^{2}b=mn+p$$

Divide both sides by x^{2}.

$$\frac{x^{2}b}{x^{2}}=\frac{mn+p}{x^{2}}$$

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

$$b=\frac{mn+p}{x^{2}}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{bx^{2}-p}{n}\text{, }&n\neq 0\\m\in \mathrm{R}\text{, }&p=bx^{2}\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 5bx^{2} from both sides.

$$-mn=p+4bx^{2}-5bx^{2}$$

Combine 4bx^{2} and -5bx^{2} to get -bx^{2}.

$$-mn=p-bx^{2}$$

The equation is in standard form.

$$\left(-n\right)m=p-bx^{2}$$

Divide both sides by -n.

$$\frac{\left(-n\right)m}{-n}=\frac{p-bx^{2}}{-n}$$

Dividing by -n undoes the multiplication by -n.

$$m=\frac{p-bx^{2}}{-n}$$

Divide p-bx^{2} by -n.

$$m=-\frac{p-bx^{2}}{n}$$