Solve ri(x)=7(2x+3)+5(x+2)(x-4)

$$r i ( x ) = 7 ( 2 x + 3 ) + 5 ( x + 2 ) ( x - 4 )$$

Solve for r

$$r=-5ix-4i+\frac{19i}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by 2x+3.

$$rix=14x+21+5\left(x+2\right)\left(x-4\right)$$

Use the distributive property to multiply 5 by x+2.

$$rix=14x+21+\left(5x+10\right)\left(x-4\right)$$

Use the distributive property to multiply 5x+10 by x-4 and combine like terms.

$$rix=14x+21+5x^{2}-10x-40$$

Combine 14x and -10x to get 4x.

$$rix=4x+21+5x^{2}-40$$

Subtract 40 from 21 to get -19.

$$rix=4x-19+5x^{2}$$

The equation is in standard form.

$$ixr=5x^{2}+4x-19$$

Divide both sides by ix.

$$\frac{ixr}{ix}=\frac{5x^{2}+4x-19}{ix}$$

Dividing by ix undoes the multiplication by ix.

$$r=\frac{5x^{2}+4x-19}{ix}$$

Divide 4x-19+5x^{2} by ix.

$$r=-5ix-4i+\frac{19i}{x}$$

Solve for x

$$x=-\frac{\sqrt{396-8ir-r^{2}}}{10}+\frac{ir}{10}-\frac{2}{5}$$

$$x=\frac{\sqrt{396-8ir-r^{2}}}{10}+\frac{ir}{10}-\frac{2}{5}$$