Solve x(5-x)+2(y-3x)=(x+3)(x-2)

$$x ( 5 - x ) + 2 ( y - 3 x ) = ( x + 3 ) ( x - 2 )$$

Solve for y

$$y=x^{2}+x-3$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 5-x.

$$5x-x^{2}+2\left(y-3x\right)=\left(x+3\right)\left(x-2\right)$$

Use the distributive property to multiply 2 by y-3x.

$$5x-x^{2}+2y-6x=\left(x+3\right)\left(x-2\right)$$

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

$$-x-x^{2}+2y=\left(x+3\right)\left(x-2\right)$$

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

$$-x-x^{2}+2y=x^{2}+x-6$$

Add x to both sides.

$$-x^{2}+2y=x^{2}+x-6+x$$

Combine x and x to get 2x.

$$-x^{2}+2y=x^{2}+2x-6$$

Add x^{2} to both sides.

$$2y=x^{2}+2x-6+x^{2}$$

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

$$2y=2x^{2}+2x-6$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{2x^{2}+2x-6}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{2x^{2}+2x-6}{2}$$

Divide 2x^{2}+2x-6 by 2.

$$y=x^{2}+x-3$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{4y+13}-1}{2}$$

$$x=\frac{\sqrt{4y+13}-1}{2}$$

Solve for x

$$x=\frac{-\sqrt{4y+13}-1}{2}$$

$$x=\frac{\sqrt{4y+13}-1}{2}\text{, }y\geq -\frac{13}{4}$$