Solve (100-x)y(1+002x)=100x

$$(100-x)y(1+002x)=100x$$

Solve for x

$$x=\frac{100y}{y+100}$$

$$y\neq -100$$

Steps for Solving Linear Equation

Multiply 0 and 0 to get 0.

$$\left(100-x\right)y\left(1+0\times 2x\right)=100x$$

Multiply 0 and 2 to get 0.

$$\left(100-x\right)y\left(1+0x\right)=100x$$

Anything times zero gives zero.

$$\left(100-x\right)y\left(1+0\right)=100x$$

Add 1 and 0 to get 1.

$$\left(100-x\right)y\times 1=100x$$

Use the distributive property to multiply 100-x by y.

$$\left(100y-xy\right)\times 1=100x$$

Use the distributive property to multiply 100y-xy by 1.

$$100y-xy=100x$$

Subtract 100x from both sides.

$$100y-xy-100x=0$$

Subtract 100y from both sides. Anything subtracted from zero gives its negation.

$$-xy-100x=-100y$$

Combine all terms containing x.

$$\left(-y-100\right)x=-100y$$

Divide both sides by -y-100.

$$\frac{\left(-y-100\right)x}{-y-100}=-\frac{100y}{-y-100}$$

Dividing by -y-100 undoes the multiplication by -y-100.

$$x=-\frac{100y}{-y-100}$$

Divide -100y by -y-100.

$$x=\frac{100y}{y+100}$$

Solve for y

$$y=\frac{100x}{100-x}$$

$$x\neq 100$$

Steps for Solving Linear Equation

Multiply 0 and 0 to get 0.

$$\left(100-x\right)y\left(1+0\times 2x\right)=100x$$

Multiply 0 and 2 to get 0.

$$\left(100-x\right)y\left(1+0x\right)=100x$$

Anything times zero gives zero.

$$\left(100-x\right)y\left(1+0\right)=100x$$

Add 1 and 0 to get 1.

$$\left(100-x\right)y\times 1=100x$$

Use the distributive property to multiply 100-x by y.

$$\left(100y-xy\right)\times 1=100x$$

Use the distributive property to multiply 100y-xy by 1.

$$100y-xy=100x$$

Combine all terms containing y.

$$\left(100-x\right)y=100x$$

Divide both sides by 100-x.

$$\frac{\left(100-x\right)y}{100-x}=\frac{100x}{100-x}$$

Dividing by 100-x undoes the multiplication by 100-x.

$$y=\frac{100x}{100-x}$$