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

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

Solve for x

$$x=\frac{3}{5}=0.6$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply -3 by x-1.

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

Combine -12x and -3x to get -15x.

$$9x^{2}-15x+4+3=\left(3x+1\right)\left(3x-1\right)-1$$

Add 4 and 3 to get 7.

$$9x^{2}-15x+7=\left(3x+1\right)\left(3x-1\right)-1$$

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.

$$9x^{2}-15x+7=\left(3x\right)^{2}-1-1$$

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

$$9x^{2}-15x+7=3^{2}x^{2}-1-1$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}-15x+7=9x^{2}-1-1$$

Subtract 1 from -1 to get -2.

$$9x^{2}-15x+7=9x^{2}-2$$

Subtract 9x^{2} from both sides.

$$9x^{2}-15x+7-9x^{2}=-2$$

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

$$-15x+7=-2$$

Subtract 7 from both sides.

$$-15x=-2-7$$

Subtract 7 from -2 to get -9.

$$-15x=-9$$

Divide both sides by -15.

$$x=\frac{-9}{-15}$$

Reduce the fraction \frac{-9}{-15} to lowest terms by extracting and canceling out -3.

$$x=\frac{3}{5}$$