Solve c=(x+1)(2+x)-(x+1)(4x-8)

$$c = ( x + 1 ) ( 2 + x ) - ( x + 1 ) ( 4 x - 8 )$$

Solve for c

$$c=\left(10-3x\right)\left(x+1\right)$$

Solution Steps

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

$$c=3x+x^{2}+2-\left(x+1\right)\left(4x-8\right)$$

Use the distributive property to multiply x+1 by 4x-8 and combine like terms.

$$c=3x+x^{2}+2-\left(4x^{2}-4x-8\right)$$

To find the opposite of 4x^{2}-4x-8, find the opposite of each term.

$$c=3x+x^{2}+2-4x^{2}+4x+8$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$c=3x-3x^{2}+2+4x+8$$

Combine 3x and 4x to get 7x.

$$c=7x-3x^{2}+2+8$$

Add 2 and 8 to get 10.

$$c=7x-3x^{2}+10$$

Solve for x (complex solution)

$$x=\frac{\sqrt{169-12c}+7}{6}$$

$$x=\frac{-\sqrt{169-12c}+7}{6}$$

Solve for x

$$x=\frac{\sqrt{169-12c}+7}{6}$$

$$x=\frac{-\sqrt{169-12c}+7}{6}\text{, }c\leq \frac{169}{12}$$