Solve (10*x+y)=5x(x+y)

$$( 10 * x + y ) = 5 x ( x + y )$$

Solve for y

$$y=-\frac{5x\left(2-x\right)}{1-5x}$$

$$x\neq \frac{1}{5}$$

Steps for Solving Linear Equation

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

$$10x+y=5x^{2}+5xy$$

Subtract 5xy from both sides.

$$10x+y-5xy=5x^{2}$$

Subtract 10x from both sides.

$$y-5xy=5x^{2}-10x$$

Combine all terms containing y.

$$\left(1-5x\right)y=5x^{2}-10x$$

Divide both sides by 1-5x.

$$\frac{\left(1-5x\right)y}{1-5x}=\frac{5x\left(x-2\right)}{1-5x}$$

Dividing by 1-5x undoes the multiplication by 1-5x.

$$y=\frac{5x\left(x-2\right)}{1-5x}$$

Solve for x

$$x=-\frac{\sqrt{25y^{2}-80y+100}}{10}-\frac{y}{2}+1$$

$$x=\frac{\sqrt{25y^{2}-80y+100}}{10}-\frac{y}{2}+1$$