Solve D=x^2-6x+9+(x-3)(2x+7)

$$D = x ^ { 2 } - 6 x + 9 + ( x - 3 ) ( 2 x + 7 )$$

Solve for D

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

Solution Steps

Use the distributive property to multiply x-3 by 2x+7 and combine like terms.

$$D=x^{2}-6x+9+2x^{2}+x-21$$

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

$$D=3x^{2}-6x+9+x-21$$

Combine -6x and x to get -5x.

$$D=3x^{2}-5x+9-21$$

Subtract 21 from 9 to get -12.

$$D=3x^{2}-5x-12$$

Solve for x (complex solution)

$$x=\frac{\sqrt{12D+169}+5}{6}$$

$$x=\frac{-\sqrt{12D+169}+5}{6}$$

Solve for x

$$x=\frac{\sqrt{12D+169}+5}{6}$$

$$x=\frac{-\sqrt{12D+169}+5}{6}\text{, }D\geq -\frac{169}{12}$$