Solve x(45-x)-(x+5)(40-x)=50

$$x ( 45 - x ) - ( x + 5 ) ( 40 - x ) = 50$$

Solve for x

$$x=25$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 45-x.

$$45x-x^{2}-\left(x+5\right)\left(40-x\right)=50$$

Use the distributive property to multiply x+5 by 40-x and combine like terms.

$$45x-x^{2}-\left(35x-x^{2}+200\right)=50$$

To find the opposite of 35x-x^{2}+200, find the opposite of each term.

$$45x-x^{2}-35x+x^{2}-200=50$$

Combine 45x and -35x to get 10x.

$$10x-x^{2}+x^{2}-200=50$$

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

$$10x-200=50$$

Add 200 to both sides.

$$10x=50+200$$

Add 50 and 200 to get 250.

$$10x=250$$

Divide both sides by 10.

$$x=\frac{250}{10}$$

Divide 250 by 10 to get 25.

$$x=25$$