Solve D(x)=(3x-12)(3-4x)-(2x-8

$$D ( x ) = ( 3 x - 12 ) ( 3 - 4 x ) - ( 2 x - 8$$

Solve for D

$$D=-12x+55-\frac{28}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x-12 by 3-4x and combine like terms.

$$Dx=57x-12x^{2}-36-\left(2x-8\right)$$

To find the opposite of 2x-8, find the opposite of each term.

$$Dx=57x-12x^{2}-36-2x+8$$

Combine 57x and -2x to get 55x.

$$Dx=55x-12x^{2}-36+8$$

Add -36 and 8 to get -28.

$$Dx=55x-12x^{2}-28$$

The equation is in standard form.

$$xD=-12x^{2}+55x-28$$

Divide both sides by x.

$$\frac{xD}{x}=\frac{\left(4-x\right)\left(12x-7\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$D=\frac{\left(4-x\right)\left(12x-7\right)}{x}$$

Divide \left(-7+12x\right)\left(4-x\right) by x.

$$D=-12x+55-\frac{28}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{D^{2}-110D+1681}-D+55}{24}$$

$$x=\frac{-\sqrt{D^{2}-110D+1681}-D+55}{24}$$

Solve for x

$$x=\frac{\sqrt{D^{2}-110D+1681}-D+55}{24}$$

$$x=\frac{-\sqrt{D^{2}-110D+1681}-D+55}{24}\text{, }D\geq 8\sqrt{21}+55\text{ or }D\leq 55-8\sqrt{21}$$