Solve (x+1)(x+4)=(x-7)(x+6)

$$( x + 1 ) ( x + 4 ) = ( x - 7 ) ( x + 6 )$$

Solve for x

$$x = -\frac{23}{3} = -7\frac{2}{3} \approx -7.666666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+1 by x+4 and combine like terms.

$$x^{2}+5x+4=\left(x-7\right)\left(x+6\right)$$

Use the distributive property to multiply x-7 by x+6 and combine like terms.

$$x^{2}+5x+4=x^{2}-x-42$$

Subtract x^{2} from both sides.

$$x^{2}+5x+4-x^{2}=-x-42$$

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

$$5x+4=-x-42$$

Add x to both sides.

$$5x+4+x=-42$$

Combine 5x and x to get 6x.

$$6x+4=-42$$

Subtract 4 from both sides.

$$6x=-42-4$$

Subtract 4 from -42 to get -46.

$$6x=-46$$

Divide both sides by 6.

$$x=\frac{-46}{6}$$

Reduce the fraction \frac{-46}{6} to lowest terms by extracting and canceling out 2.

$$x=-\frac{23}{3}$$