Solve x(9x-5)-(3x+1)(3x-1)=6

$$x ( 9 x - 5 ) - ( 3 x + 1 ) ( 3 x - 1 ) = 6$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 9x-5.

$$9x^{2}-5x-\left(3x+1\right)\left(3x-1\right)=6$$

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.

$$9x^{2}-5x-\left(\left(3x\right)^{2}-1\right)=6$$

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

$$9x^{2}-5x-\left(3^{2}x^{2}-1\right)=6$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}-5x-\left(9x^{2}-1\right)=6$$

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

$$9x^{2}-5x-9x^{2}+1=6$$

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

$$-5x+1=6$$

Subtract 1 from both sides.

$$-5x=6-1$$

Subtract 1 from 6 to get 5.

$$-5x=5$$

Divide both sides by -5.

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

Divide 5 by -5 to get -1.

$$x=-1$$