Solve (2x-3)(2x+3)-4x(x+1)=2(x+3)+3

$$(2x-3)(2x+3)-4x(x+1)=2(x+3)+3$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Consider \left(2x-3\right)\left(2x+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$\left(2x\right)^{2}-9-4x\left(x+1\right)=2\left(x+3\right)+3$$

Expand \left(2x\right)^{2}.

$$2^{2}x^{2}-9-4x\left(x+1\right)=2\left(x+3\right)+3$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-9-4x\left(x+1\right)=2\left(x+3\right)+3$$

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

$$4x^{2}-9-4x\left(x+1\right)=2x+6+3$$

Add 6 and 3 to get 9.

$$4x^{2}-9-4x\left(x+1\right)=2x+9$$

Subtract 2x from both sides.

$$4x^{2}-9-4x\left(x+1\right)-2x=9$$

Use the distributive property to multiply -4x by x+1.

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

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

$$-9-4x-2x=9$$

Combine -4x and -2x to get -6x.

$$-9-6x=9$$

Add 9 to both sides.

$$-6x=9+9$$

Add 9 and 9 to get 18.

$$-6x=18$$

Divide both sides by -6.

$$x=\frac{18}{-6}$$

Divide 18 by -6 to get -3.

$$x=-3$$