Solve F=(x+1)(x-3)-(x+1)(3x+7)

$$F = ( x + 1 ) ( x - 3 ) - ( x + 1 ) ( 3 x + 7 )$$

Solve for F

$$F=-2\left(x+1\right)\left(x+5\right)$$

Solution Steps

Use the distributive property to multiply x+1 by x-3 and combine like terms.

$$F=x^{2}-2x-3-\left(x+1\right)\left(3x+7\right)$$

Use the distributive property to multiply x+1 by 3x+7 and combine like terms.

$$F=x^{2}-2x-3-\left(3x^{2}+10x+7\right)$$

To find the opposite of 3x^{2}+10x+7, find the opposite of each term.

$$F=x^{2}-2x-3-3x^{2}-10x-7$$

Combine x^{2} and -3x^{2} to get -2x^{2}.

$$F=-2x^{2}-2x-3-10x-7$$

Combine -2x and -10x to get -12x.

$$F=-2x^{2}-12x-3-7$$

Subtract 7 from -3 to get -10.

$$F=-2x^{2}-12x-10$$

Solve for x (complex solution)

$$x=\frac{\sqrt{16-2F}}{2}-3$$

$$x=-\frac{\sqrt{16-2F}}{2}-3$$

Solve for x

$$x=\frac{\sqrt{16-2F}}{2}-3$$

$$x=-\frac{\sqrt{16-2F}}{2}-3\text{, }F\leq 8$$