Solve (x-3)(x+3)+1-3x=(x-2)(x+2)+4x-5

$$( x - 3 ) ( x + 3 ) + 1 - 3 x = ( x - 2 ) ( x + 2 ) + 4 x - 5$$

Solve for x

$$x=\frac{1}{7}\approx 0.142857143$$

Steps for Solving Linear Equation

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

$$x^{2}-9+1-3x=\left(x-2\right)\left(x+2\right)+4x-5$$

Add -9 and 1 to get -8.

$$x^{2}-8-3x=\left(x-2\right)\left(x+2\right)+4x-5$$

Consider \left(x-2\right)\left(x+2\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 2.

$$x^{2}-8-3x=x^{2}-4+4x-5$$

Subtract 5 from -4 to get -9.

$$x^{2}-8-3x=x^{2}-9+4x$$

Subtract x^{2} from both sides.

$$x^{2}-8-3x-x^{2}=-9+4x$$

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

$$-8-3x=-9+4x$$

Subtract 4x from both sides.

$$-8-3x-4x=-9$$

Combine -3x and -4x to get -7x.

$$-8-7x=-9$$

Add 8 to both sides.

$$-7x=-9+8$$

Add -9 and 8 to get -1.

$$-7x=-1$$

Divide both sides by -7.

$$x=\frac{-1}{-7}$$

Fraction \frac{-1}{-7} can be simplified to \frac{1}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1}{7}$$