Solve (x+5)(5-x)=(12+x)(4-x)+1

$$(x+5)(5-x)=(12+x)(4-x)+1$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Consider \left(x+5\right)\left(5-x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 5.

$$25-x^{2}=\left(12+x\right)\left(4-x\right)+1$$

Use the distributive property to multiply 12+x by 4-x and combine like terms.

$$25-x^{2}=48-8x-x^{2}+1$$

Add 48 and 1 to get 49.

$$25-x^{2}=49-8x-x^{2}$$

Add 8x to both sides.

$$25-x^{2}+8x=49-x^{2}$$

Add x^{2} to both sides.

$$25-x^{2}+8x+x^{2}=49$$

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

$$25+8x=49$$

Subtract 25 from both sides.

$$8x=49-25$$

Subtract 25 from 49 to get 24.

$$8x=24$$

Divide both sides by 8.

$$x=\frac{24}{8}$$

Divide 24 by 8 to get 3.

$$x=3$$