Solve 2(x-3)-x(x-2)=(3-x)(x-2)-x

$$2 ( x - 3 ) - x ( x - 2 ) = ( 3 - x ) ( x - 2 ) - x$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

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

$$2x-6-x\left(x-2\right)=\left(3-x\right)\left(x-2\right)-x$$

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

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

To find the opposite of x^{2}-2x, find the opposite of each term.

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

Combine 2x and 2x to get 4x.

$$4x-6-x^{2}=\left(3-x\right)\left(x-2\right)-x$$

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

$$4x-6-x^{2}=5x-6-x^{2}-x$$

Combine 5x and -x to get 4x.

$$4x-6-x^{2}=4x-6-x^{2}$$

Subtract 4x from both sides.

$$4x-6-x^{2}-4x=-6-x^{2}$$

Combine 4x and -4x to get 0.

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

Add x^{2} to both sides.

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

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

$$-6=-6$$

Compare -6 and -6.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

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

$$2x-6-x\left(x-2\right)=\left(3-x\right)\left(x-2\right)-x$$

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

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

To find the opposite of x^{2}-2x, find the opposite of each term.

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

Combine 2x and 2x to get 4x.

$$4x-6-x^{2}=\left(3-x\right)\left(x-2\right)-x$$

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

$$4x-6-x^{2}=5x-6-x^{2}-x$$

Combine 5x and -x to get 4x.

$$4x-6-x^{2}=4x-6-x^{2}$$

Subtract 4x from both sides.

$$4x-6-x^{2}-4x=-6-x^{2}$$

Combine 4x and -4x to get 0.

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

Add x^{2} to both sides.

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

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

$$-6=-6$$

Compare -6 and -6.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$