Solve (1800+x)(800-x)=(1800-x)(800+x)

$$( 1800 + x ) ( 800 - x ) = ( 1800 - x ) ( 800 + x )$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1800+x by 800-x and combine like terms.

$$1440000-1000x-x^{2}=\left(1800-x\right)\left(800+x\right)$$

Use the distributive property to multiply 1800-x by 800+x and combine like terms.

$$1440000-1000x-x^{2}=1440000+1000x-x^{2}$$

Subtract 1000x from both sides.

$$1440000-1000x-x^{2}-1000x=1440000-x^{2}$$

Combine -1000x and -1000x to get -2000x.

$$1440000-2000x-x^{2}=1440000-x^{2}$$

Add x^{2} to both sides.

$$1440000-2000x-x^{2}+x^{2}=1440000$$

Combine -x^{2} and x^{2} to get 0.

$$1440000-2000x=1440000$$

Subtract 1440000 from both sides.

$$-2000x=1440000-1440000$$

Subtract 1440000 from 1440000 to get 0.

$$-2000x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -2000 is not equal to 0, x must be equal to 0.

$$x=0$$