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

$$( 2 - 3 x ) ^ { 2 } - ( 3 x - 1 ) ( 3 x + 1 ) = 2$$

Solve for x

$$x=\frac{1}{4}=0.25$$

Steps for Solving Linear Equation

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

$$4-12x+9x^{2}-\left(3x-1\right)\left(3x+1\right)=2$$

Consider \left(3x-1\right)\left(3x+1\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 1.

$$4-12x+9x^{2}-\left(\left(3x\right)^{2}-1\right)=2$$

Expand \left(3x\right)^{2}.

$$4-12x+9x^{2}-\left(3^{2}x^{2}-1\right)=2$$

Calculate 3 to the power of 2 and get 9.

$$4-12x+9x^{2}-\left(9x^{2}-1\right)=2$$

To find the opposite of 9x^{2}-1, find the opposite of each term.

$$4-12x+9x^{2}-9x^{2}+1=2$$

Combine 9x^{2} and -9x^{2} to get 0.

$$4-12x+1=2$$

Add 4 and 1 to get 5.

$$5-12x=2$$

Subtract 5 from both sides.

$$-12x=2-5$$

Subtract 5 from 2 to get -3.

$$-12x=-3$$

Divide both sides by -12.

$$x=\frac{-3}{-12}$$

Reduce the fraction \frac{-3}{-12} to lowest terms by extracting and canceling out -3.

$$x=\frac{1}{4}$$