Solve (x+y)(4x-2y)=-(x-y)(4x-2y)

$$(x+y)(4x-2y)=-(x-y)(4x-2y)$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=2x\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+y by 4x-2y and combine like terms.

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

To find the opposite of x-y, find the opposite of each term.

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

Use the distributive property to multiply -x+y by 4x-2y and combine like terms.

$$4x^{2}+2xy-2y^{2}=-4x^{2}+6xy-2y^{2}$$

Subtract 6xy from both sides.

$$4x^{2}+2xy-2y^{2}-6xy=-4x^{2}-2y^{2}$$

Combine 2xy and -6xy to get -4xy.

$$4x^{2}-4xy-2y^{2}=-4x^{2}-2y^{2}$$

Add 2y^{2} to both sides.

$$4x^{2}-4xy-2y^{2}+2y^{2}=-4x^{2}$$

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

$$4x^{2}-4xy=-4x^{2}$$

Subtract 4x^{2} from both sides.

$$-4xy=-4x^{2}-4x^{2}$$

Combine -4x^{2} and -4x^{2} to get -8x^{2}.

$$-4xy=-8x^{2}$$

The equation is in standard form.

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

Divide both sides by -4x.

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

Dividing by -4x undoes the multiplication by -4x.

$$y=-\frac{8x^{2}}{-4x}$$

Divide -8x^{2} by -4x.

$$y=2x$$

Solve for y

$$\left\{\begin{matrix}\\y=2x\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+y by 4x-2y and combine like terms.

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

To find the opposite of x-y, find the opposite of each term.

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

Use the distributive property to multiply -x+y by 4x-2y and combine like terms.

$$4x^{2}+2xy-2y^{2}=-4x^{2}+6xy-2y^{2}$$

Subtract 6xy from both sides.

$$4x^{2}+2xy-2y^{2}-6xy=-4x^{2}-2y^{2}$$

Combine 2xy and -6xy to get -4xy.

$$4x^{2}-4xy-2y^{2}=-4x^{2}-2y^{2}$$

Add 2y^{2} to both sides.

$$4x^{2}-4xy-2y^{2}+2y^{2}=-4x^{2}$$

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

$$4x^{2}-4xy=-4x^{2}$$

Subtract 4x^{2} from both sides.

$$-4xy=-4x^{2}-4x^{2}$$

Combine -4x^{2} and -4x^{2} to get -8x^{2}.

$$-4xy=-8x^{2}$$

The equation is in standard form.

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

Divide both sides by -4x.

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

Dividing by -4x undoes the multiplication by -4x.

$$y=-\frac{8x^{2}}{-4x}$$

Divide -8x^{2} by -4x.

$$y=2x$$

Solve for x

$$x=\frac{y}{2}$$

$$x=0$$