Solve 5x*6+2*4div6x+4=25yxyz^2

$$5x \times 6+2 \times 4 \div 6x+4=25yxy { z }^{ 2 }$$

Solve for x (complex solution)

$$x=-\frac{12}{94-75\left(yz\right)^{2}}$$

$$z=0\text{ or }\left(y\neq -\frac{\sqrt{282}}{15z}\text{ and }y\neq \frac{\sqrt{282}}{15z}\right)$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6.

$$30x\times 6+2\times 4x+24=150yxyz^{2}$$

Multiply y and y to get y^{2}.

$$30x\times 6+2\times 4x+24=150y^{2}xz^{2}$$

Multiply 30 and 6 to get 180.

$$180x+2\times 4x+24=150y^{2}xz^{2}$$

Multiply 2 and 4 to get 8.

$$180x+8x+24=150y^{2}xz^{2}$$

Combine 180x and 8x to get 188x.

$$188x+24=150y^{2}xz^{2}$$

Subtract 150y^{2}xz^{2} from both sides.

$$188x+24-150y^{2}xz^{2}=0$$

Subtract 24 from both sides. Anything subtracted from zero gives its negation.

$$188x-150y^{2}xz^{2}=-24$$

Combine all terms containing x.

$$\left(188-150y^{2}z^{2}\right)x=-24$$

Divide both sides by 188-150y^{2}z^{2}.

$$\frac{\left(188-150y^{2}z^{2}\right)x}{188-150y^{2}z^{2}}=-\frac{24}{188-150y^{2}z^{2}}$$

Dividing by 188-150y^{2}z^{2} undoes the multiplication by 188-150y^{2}z^{2}.

$$x=-\frac{24}{188-150y^{2}z^{2}}$$

Divide -24 by 188-150y^{2}z^{2}.

$$x=-\frac{12}{94-75y^{2}z^{2}}$$

Solve for x

$$x=-\frac{12}{94-75\left(yz\right)^{2}}$$

$$|y|\neq \frac{\sqrt{282}}{15|z|}\text{ or }z=0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6.

$$30x\times 6+2\times 4x+24=150yxyz^{2}$$

Multiply y and y to get y^{2}.

$$30x\times 6+2\times 4x+24=150y^{2}xz^{2}$$

Multiply 30 and 6 to get 180.

$$180x+2\times 4x+24=150y^{2}xz^{2}$$

Multiply 2 and 4 to get 8.

$$180x+8x+24=150y^{2}xz^{2}$$

Combine 180x and 8x to get 188x.

$$188x+24=150y^{2}xz^{2}$$

Subtract 150y^{2}xz^{2} from both sides.

$$188x+24-150y^{2}xz^{2}=0$$

Subtract 24 from both sides. Anything subtracted from zero gives its negation.

$$188x-150y^{2}xz^{2}=-24$$

Combine all terms containing x.

$$\left(188-150y^{2}z^{2}\right)x=-24$$

Divide both sides by 188-150y^{2}z^{2}.

$$\frac{\left(188-150y^{2}z^{2}\right)x}{188-150y^{2}z^{2}}=-\frac{24}{188-150y^{2}z^{2}}$$

Dividing by 188-150y^{2}z^{2} undoes the multiplication by 188-150y^{2}z^{2}.

$$x=-\frac{24}{188-150y^{2}z^{2}}$$

Divide -24 by 188-150y^{2}z^{2}.

$$x=-\frac{12}{94-75y^{2}z^{2}}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=-\frac{ix^{-\frac{1}{2}}\sqrt{-282x-36}}{15z}\text{; }y=\frac{ix^{-\frac{1}{2}}\sqrt{-282x-36}}{15z}\text{, }&z\neq 0\text{ and }x\neq 0\\y\in \mathrm{C}\text{, }&x=-\frac{6}{47}\text{ and }z=0\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=\frac{\sqrt{282+\frac{36}{x}}}{15|z|}\text{; }y=-\frac{\sqrt{282+\frac{36}{x}}}{15|z|}\text{, }&\left(x\leq -\frac{6}{47}\text{ or }x>0\right)\text{ and }z\neq 0\\y\in \mathrm{R}\text{, }&x=-\frac{6}{47}\text{ and }z=0\end{matrix}\right.$$