Solve D=9x^2+12x+4-(-5-x)(3x+2)

$$D = 9 x ^ { 2 } + 12 x + 4 - ( - 5 - x ) ( 3 x + 2 )$$

Solve for D

$$D=\left(3x+2\right)\left(4x+7\right)$$

Solution Steps

Use the distributive property to multiply -5-x by 3x+2 and combine like terms.

$$D=9x^{2}+12x+4-\left(-17x-10-3x^{2}\right)$$

To find the opposite of -17x-10-3x^{2}, find the opposite of each term.

$$D=9x^{2}+12x+4+17x+10+3x^{2}$$

Combine 12x and 17x to get 29x.

$$D=9x^{2}+29x+4+10+3x^{2}$$

Add 4 and 10 to get 14.

$$D=9x^{2}+29x+14+3x^{2}$$

Combine 9x^{2} and 3x^{2} to get 12x^{2}.

$$D=12x^{2}+29x+14$$

Solve for x (complex solution)

$$x=\frac{\sqrt{48D+169}-29}{24}$$

$$x=\frac{-\sqrt{48D+169}-29}{24}$$

Solve for x

$$x=\frac{\sqrt{48D+169}-29}{24}$$

$$x=\frac{-\sqrt{48D+169}-29}{24}\text{, }D\geq -\frac{169}{48}$$