Solve 7x-5y(x+36y)=7

$$7x-5y(x+36y)=7$$

Solve for x

$$x=\frac{180y^{2}+7}{7-5y}$$

$$y\neq \frac{7}{5}$$

Steps for Solving Linear Equation

Multiply -1 and 5 to get -5.

$$7x-5y\left(x+36y\right)=7$$

Use the distributive property to multiply -5y by x+36y.

$$7x-5yx-180y^{2}=7$$

Add 180y^{2} to both sides.

$$7x-5yx=7+180y^{2}$$

Combine all terms containing x.

$$\left(7-5y\right)x=7+180y^{2}$$

The equation is in standard form.

$$\left(7-5y\right)x=180y^{2}+7$$

Divide both sides by -5y+7.

$$\frac{\left(7-5y\right)x}{7-5y}=\frac{180y^{2}+7}{7-5y}$$

Dividing by -5y+7 undoes the multiplication by -5y+7.

$$x=\frac{180y^{2}+7}{7-5y}$$

Solve for y (complex solution)

$$y=\frac{\sqrt{25x^{2}+5040x-5040}}{360}-\frac{x}{72}$$

$$y=-\frac{\sqrt{25x^{2}+5040x-5040}}{360}-\frac{x}{72}$$

Solve for y

$$y=\frac{\sqrt{25x^{2}+5040x-5040}}{360}-\frac{x}{72}$$

$$y=-\frac{\sqrt{25x^{2}+5040x-5040}}{360}-\frac{x}{72}\text{, }x\geq \frac{12\sqrt{1799}-504}{5}\text{ or }x\leq \frac{-12\sqrt{1799}-504}{5}$$