Solve 4x^2+12x+9/2x+3=2x+3

$$\frac { 4 x ^ { 2 } + 12 x + 9 } { 2 x + 3 } = 2 x + 3$$

Solve for x

$$x\neq -\frac{3}{2}$$

Solution Steps

Variable x cannot be equal to -\frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by 2x+3.

$$4x^{2}+12x+9=2x\left(2x+3\right)+\left(2x+3\right)\times 3$$

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

$$4x^{2}+12x+9=4x^{2}+6x+\left(2x+3\right)\times 3$$

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

$$4x^{2}+12x+9=4x^{2}+6x+6x+9$$

Combine 6x and 6x to get 12x.

$$4x^{2}+12x+9=4x^{2}+12x+9$$

Subtract 4x^{2} from both sides.

$$4x^{2}+12x+9-4x^{2}=12x+9$$

Combine 4x^{2} and -4x^{2} to get 0.

$$12x+9=12x+9$$

Subtract 12x from both sides.

$$12x+9-12x=9$$

Combine 12x and -12x to get 0.

$$9=9$$

Compare 9 and 9.

$$\text{true}$$

This is true for any x.

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

Variable x cannot be equal to -\frac{3}{2}.

$$x\in \mathrm{R}\setminus -\frac{3}{2}$$