Solve (14+x)(14-x)=(x-17)(76-x)

$$( 14 + x ) ( 14 - x ) = ( x - 17 ) ( 76 - x )$$

Solve for x

$$x=16$$

Steps for Solving Linear Equation

Consider \left(14+x\right)\left(14-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 14.

$$196-x^{2}=\left(x-17\right)\left(76-x\right)$$

Use the distributive property to multiply x-17 by 76-x and combine like terms.

$$196-x^{2}=93x-x^{2}-1292$$

Subtract 93x from both sides.

$$196-x^{2}-93x=-x^{2}-1292$$

Add x^{2} to both sides.

$$196-x^{2}-93x+x^{2}=-1292$$

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

$$196-93x=-1292$$

Subtract 196 from both sides.

$$-93x=-1292-196$$

Subtract 196 from -1292 to get -1488.

$$-93x=-1488$$

Divide both sides by -93.

$$x=\frac{-1488}{-93}$$

Divide -1488 by -93 to get 16.

$$x=16$$