Solve 6/4x^2+12x+9+4x/2x+3=2

$$\frac { 6 } { 4 x ^ { 2 } + 12 x + 9 } + \frac { 4 x } { 2 x + 3 } = 2$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by \left(2x+3\right)^{2}, the least common multiple of 4x^{2}+12x+9,2x+3.

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

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

$$6+\left(8x+12\right)x=2\left(2x+3\right)^{2}$$

Use the distributive property to multiply 8x+12 by x.

$$6+8x^{2}+12x=2\left(2x+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+3\right)^{2}.

$$6+8x^{2}+12x=2\left(4x^{2}+12x+9\right)$$

Use the distributive property to multiply 2 by 4x^{2}+12x+9.

$$6+8x^{2}+12x=8x^{2}+24x+18$$

Subtract 8x^{2} from both sides.

$$6+8x^{2}+12x-8x^{2}=24x+18$$

Combine 8x^{2} and -8x^{2} to get 0.

$$6+12x=24x+18$$

Subtract 24x from both sides.

$$6+12x-24x=18$$

Combine 12x and -24x to get -12x.

$$6-12x=18$$

Subtract 6 from both sides.

$$-12x=18-6$$

Subtract 6 from 18 to get 12.

$$-12x=12$$

Divide both sides by -12.

$$x=\frac{12}{-12}$$

Divide 12 by -12 to get -1.

$$x=-1$$