Solve B=(x+1)(x+2)-5(x+2)

$$B = ( x + 1 ) ( x + 2 ) - 5 ( x + 2 )$$

Solve for B

$$B=\left(x-4\right)\left(x+2\right)$$

Solution Steps

Use the distributive property to multiply x+1 by x+2 and combine like terms.

$$B=x^{2}+3x+2-5\left(x+2\right)$$

Use the distributive property to multiply -5 by x+2.

$$B=x^{2}+3x+2-5x-10$$

Combine 3x and -5x to get -2x.

$$B=x^{2}-2x+2-10$$

Subtract 10 from 2 to get -8.

$$B=x^{2}-2x-8$$

Solve for x (complex solution)

$$x=-\sqrt{B+9}+1$$

$$x=\sqrt{B+9}+1$$

Solve for x

$$x=-\sqrt{B+9}+1$$

$$x=\sqrt{B+9}+1\text{, }B\geq -9$$