Solve 2x(x+2)=x(2x+1)

$$2 x ( x + 2 ) = x ( 2 x + 1 )$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

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

$$2x^{2}+4x=x\left(2x+1\right)$$

Use the distributive property to multiply x by 2x+1.

$$2x^{2}+4x=2x^{2}+x$$

Subtract 2x^{2} from both sides.

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

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

$$4x=x$$

Subtract x from both sides.

$$4x-x=0$$

Combine 4x and -x to get 3x.

$$3x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 3 is not equal to 0, x must be equal to 0.

$$x=0$$