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

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

Solve for x

$$x = -\frac{8}{3} = -2\frac{2}{3} \approx -2.666666667$$

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.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Use the distributive property to multiply 4x-1 by x+1 and combine like terms.

$$4x^{2}-9=4x^{2}+3x-1$$

Subtract 4x^{2} from both sides.

$$4x^{2}-9-4x^{2}=3x-1$$

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

$$-9=3x-1$$

Swap sides so that all variable terms are on the left hand side.

$$3x-1=-9$$

Add 1 to both sides.

$$3x=-9+1$$

Add -9 and 1 to get -8.

$$3x=-8$$

Divide both sides by 3.

$$x=\frac{-8}{3}$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$x=-\frac{8}{3}$$