Solve left(2x+3right)^2-(2x-3)(2x+3)=6x

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

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

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

$$4x^{2}+12x+9-\left(2x-3\right)\left(2x+3\right)=6x$$

Consider \left(2x-3\right)\left(2x+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.

$$4x^{2}+12x+9-\left(\left(2x\right)^{2}-9\right)=6x$$

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

$$4x^{2}+12x+9-\left(2^{2}x^{2}-9\right)=6x$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}+12x+9-\left(4x^{2}-9\right)=6x$$

To find the opposite of 4x^{2}-9, find the opposite of each term.

$$4x^{2}+12x+9-4x^{2}+9=6x$$

Combine 4x^{2} and -4x^{2} to get 0.

$$12x+9+9=6x$$

Add 9 and 9 to get 18.

$$12x+18=6x$$

Subtract 6x from both sides.

$$12x+18-6x=0$$

Combine 12x and -6x to get 6x.

$$6x+18=0$$

Subtract 18 from both sides. Anything subtracted from zero gives its negation.

$$6x=-18$$

Divide both sides by 6.

$$x=\frac{-18}{6}$$

Divide -18 by 6 to get -3.

$$x=-3$$