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

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x-2 by 3x+4 and combine like terms.

$$9x^{2}+6x-8-\left(3x-5\right)^{2}=3$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-5\right)^{2}.

$$9x^{2}+6x-8-\left(9x^{2}-30x+25\right)=3$$

To find the opposite of 9x^{2}-30x+25, find the opposite of each term.

$$9x^{2}+6x-8-9x^{2}+30x-25=3$$

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

$$6x-8+30x-25=3$$

Combine 6x and 30x to get 36x.

$$36x-8-25=3$$

Subtract 25 from -8 to get -33.

$$36x-33=3$$

Add 33 to both sides.

$$36x=3+33$$

Add 3 and 33 to get 36.

$$36x=36$$

Divide both sides by 36.

$$x=\frac{36}{36}$$

Divide 36 by 36 to get 1.

$$x=1$$