Solve 12x^2+8x=4x(3x+2)

$$12 x ^ { 2 } + 8 x = 4 x ( 3 x + 2 )$$

Solve for x (complex solution)

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

Solution Steps

Use the distributive property to multiply 4x by 3x+2.

$$12x^{2}+8x=12x^{2}+8x$$

Subtract 12x^{2} from both sides.

$$12x^{2}+8x-12x^{2}=8x$$

Combine 12x^{2} and -12x^{2} to get 0.

$$8x=8x$$

Subtract 8x from both sides.

$$8x-8x=0$$

Combine 8x and -8x to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

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 4x by 3x+2.

$$12x^{2}+8x=12x^{2}+8x$$

Subtract 12x^{2} from both sides.

$$12x^{2}+8x-12x^{2}=8x$$

Combine 12x^{2} and -12x^{2} to get 0.

$$8x=8x$$

Subtract 8x from both sides.

$$8x-8x=0$$

Combine 8x and -8x to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

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