Solve y+(x-a)(x+5a)=(x-1)(x+9)-4

$$y + ( x - a ) ( x + 5 a ) = ( x - 1 ) ( x + 9 ) - 4$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{y-5a^{2}+13}{4\left(a-2\right)}\text{, }&a\neq 2\\x\in \mathrm{C}\text{, }&y=7\text{ and }a=2\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y+x^{2}+4xa-5a^{2}=\left(x-1\right)\left(x+9\right)-4$$

Use the distributive property to multiply x-1 by x+9 and combine like terms.

$$y+x^{2}+4xa-5a^{2}=x^{2}+8x-9-4$$

Subtract 4 from -9 to get -13.

$$y+x^{2}+4xa-5a^{2}=x^{2}+8x-13$$

Subtract x^{2} from both sides.

$$y+x^{2}+4xa-5a^{2}-x^{2}=8x-13$$

Combine x^{2} and -x^{2} to get 0.

$$y+4xa-5a^{2}=8x-13$$

Subtract 8x from both sides.

$$y+4xa-5a^{2}-8x=-13$$

Subtract y from both sides.

$$4xa-5a^{2}-8x=-13-y$$

Add 5a^{2} to both sides.

$$4xa-8x=-13-y+5a^{2}$$

Combine all terms containing x.

$$\left(4a-8\right)x=-13-y+5a^{2}$$

The equation is in standard form.

$$\left(4a-8\right)x=-y+5a^{2}-13$$

Divide both sides by -8+4a.

$$\frac{\left(4a-8\right)x}{4a-8}=\frac{-y+5a^{2}-13}{4a-8}$$

Dividing by -8+4a undoes the multiplication by -8+4a.

$$x=\frac{-y+5a^{2}-13}{4a-8}$$

Divide -13-y+5a^{2} by -8+4a.

$$x=\frac{-y+5a^{2}-13}{4\left(a-2\right)}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{y-5a^{2}+13}{4\left(a-2\right)}\text{, }&a\neq 2\\x\in \mathrm{R}\text{, }&y=7\text{ and }a=2\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y+x^{2}+4xa-5a^{2}=\left(x-1\right)\left(x+9\right)-4$$

Use the distributive property to multiply x-1 by x+9 and combine like terms.

$$y+x^{2}+4xa-5a^{2}=x^{2}+8x-9-4$$

Subtract 4 from -9 to get -13.

$$y+x^{2}+4xa-5a^{2}=x^{2}+8x-13$$

Subtract x^{2} from both sides.

$$y+x^{2}+4xa-5a^{2}-x^{2}=8x-13$$

Combine x^{2} and -x^{2} to get 0.

$$y+4xa-5a^{2}=8x-13$$

Subtract 8x from both sides.

$$y+4xa-5a^{2}-8x=-13$$

Subtract y from both sides.

$$4xa-5a^{2}-8x=-13-y$$

Add 5a^{2} to both sides.

$$4xa-8x=-13-y+5a^{2}$$

Combine all terms containing x.

$$\left(4a-8\right)x=-13-y+5a^{2}$$

The equation is in standard form.

$$\left(4a-8\right)x=-y+5a^{2}-13$$

Divide both sides by -8+4a.

$$\frac{\left(4a-8\right)x}{4a-8}=\frac{-y+5a^{2}-13}{4a-8}$$

Dividing by -8+4a undoes the multiplication by -8+4a.

$$x=\frac{-y+5a^{2}-13}{4a-8}$$

Divide -13-y+5a^{2} by -8+4a.

$$x=\frac{-y+5a^{2}-13}{4\left(a-2\right)}$$

Solve for a (complex solution)

$$a=\frac{-\sqrt{4x^{2}-40x+5y+65}+2x}{5}$$

$$a=\frac{\sqrt{4x^{2}-40x+5y+65}+2x}{5}$$

Solve for a

$$a=\frac{-\sqrt{4x^{2}-40x+5y+65}+2x}{5}$$

$$a=\frac{\sqrt{4x^{2}-40x+5y+65}+2x}{5}\text{, }y\geq -\frac{4x^{2}}{5}+8x-13$$