Solve 40000-400(a+b)+2ab=0

$$40000 - 400 ( a + b ) + 2 a b = 0$$

Solve for a

$$a=-\frac{200\left(100-b\right)}{b-200}$$

$$b\neq 200$$

Steps for Solving Linear Equation

Use the distributive property to multiply -400 by a+b.

$$40000-400a-400b+2ab=0$$

Subtract 40000 from both sides. Anything subtracted from zero gives its negation.

$$-400a-400b+2ab=-40000$$

Add 400b to both sides.

$$-400a+2ab=-40000+400b$$

Combine all terms containing a.

$$\left(-400+2b\right)a=-40000+400b$$

The equation is in standard form.

$$\left(2b-400\right)a=400b-40000$$

Divide both sides by -400+2b.

$$\frac{\left(2b-400\right)a}{2b-400}=\frac{400b-40000}{2b-400}$$

Dividing by -400+2b undoes the multiplication by -400+2b.

$$a=\frac{400b-40000}{2b-400}$$

Divide -40000+400b by -400+2b.

$$a=\frac{200\left(b-100\right)}{b-200}$$

Solve for b

$$b=-\frac{200\left(100-a\right)}{a-200}$$

$$a\neq 200$$

Steps for Solving Linear Equation

Use the distributive property to multiply -400 by a+b.

$$40000-400a-400b+2ab=0$$

Subtract 40000 from both sides. Anything subtracted from zero gives its negation.

$$-400a-400b+2ab=-40000$$

Add 400a to both sides.

$$-400b+2ab=-40000+400a$$

Combine all terms containing b.

$$\left(-400+2a\right)b=-40000+400a$$

The equation is in standard form.

$$\left(2a-400\right)b=400a-40000$$

Divide both sides by -400+2a.

$$\frac{\left(2a-400\right)b}{2a-400}=\frac{400a-40000}{2a-400}$$

Dividing by -400+2a undoes the multiplication by -400+2a.

$$b=\frac{400a-40000}{2a-400}$$

Divide -40000+400a by -400+2a.

$$b=\frac{200\left(a-100\right)}{a-200}$$