Solve (x+y)*(x+8y+10)=(x+6y-4)^2

$$( x + y ) \cdot ( x + 8 y + 10 ) = ( x + 6 y - 4 ) ^ { 2 }$$

Solve for x

$$x=-\frac{2\left(-14y^{2}+29y-8\right)}{3\left(6-y\right)}$$

$$y\neq 6$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+y by x+8y+10 and combine like terms.

$$x^{2}+9xy+10x+8y^{2}+10y=\left(x+6y-4\right)^{2}$$

Square x+6y-4.

$$x^{2}+9xy+10x+8y^{2}+10y=x^{2}+12xy-8x+36y^{2}-48y+16$$

Subtract x^{2} from both sides.

$$x^{2}+9xy+10x+8y^{2}+10y-x^{2}=12xy-8x+36y^{2}-48y+16$$

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

$$9xy+10x+8y^{2}+10y=12xy-8x+36y^{2}-48y+16$$

Subtract 12xy from both sides.

$$9xy+10x+8y^{2}+10y-12xy=-8x+36y^{2}-48y+16$$

Combine 9xy and -12xy to get -3xy.

$$-3xy+10x+8y^{2}+10y=-8x+36y^{2}-48y+16$$

Add 8x to both sides.

$$-3xy+10x+8y^{2}+10y+8x=36y^{2}-48y+16$$

Combine 10x and 8x to get 18x.

$$-3xy+18x+8y^{2}+10y=36y^{2}-48y+16$$

Subtract 8y^{2} from both sides.

$$-3xy+18x+10y=36y^{2}-48y+16-8y^{2}$$

Combine 36y^{2} and -8y^{2} to get 28y^{2}.

$$-3xy+18x+10y=28y^{2}-48y+16$$

Subtract 10y from both sides.

$$-3xy+18x=28y^{2}-48y+16-10y$$

Combine -48y and -10y to get -58y.

$$-3xy+18x=28y^{2}-58y+16$$

Combine all terms containing x.

$$\left(-3y+18\right)x=28y^{2}-58y+16$$

The equation is in standard form.

$$\left(18-3y\right)x=28y^{2}-58y+16$$

Divide both sides by -3y+18.

$$\frac{\left(18-3y\right)x}{18-3y}=\frac{28y^{2}-58y+16}{18-3y}$$

Dividing by -3y+18 undoes the multiplication by -3y+18.

$$x=\frac{28y^{2}-58y+16}{18-3y}$$

Divide 28y^{2}-58y+16 by -3y+18.

$$x=\frac{2\left(14y^{2}-29y+8\right)}{3\left(6-y\right)}$$

Solve for y (complex solution)

$$y=-\frac{\sqrt{9x^{2}+1668x+1572}}{56}-\frac{3x}{56}+\frac{29}{28}$$

$$y=\frac{\sqrt{9x^{2}+1668x+1572}}{56}-\frac{3x}{56}+\frac{29}{28}$$

Solve for y

$$y=-\frac{\sqrt{9x^{2}+1668x+1572}}{56}-\frac{3x}{56}+\frac{29}{28}$$

$$y=\frac{\sqrt{9x^{2}+1668x+1572}}{56}-\frac{3x}{56}+\frac{29}{28}\text{, }x\geq \frac{104\sqrt{7}-278}{3}\text{ or }x\leq \frac{-104\sqrt{7}-278}{3}$$