Solve left(2x+3right)^2-left(2x+5right)left(2x-5right)=38

$${ \left(2x+3 \right) }^{ 2 } - \left( 2x+5 \right) \left( 2x-5 \right) = 38$$

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

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}.

$$4x^{2}+12x+9-\left(2x+5\right)\left(2x-5\right)=38$$

Consider \left(2x+5\right)\left(2x-5\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 5.

$$4x^{2}+12x+9-\left(\left(2x\right)^{2}-25\right)=38$$

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

$$4x^{2}+12x+9-\left(2^{2}x^{2}-25\right)=38$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}+12x+9-\left(4x^{2}-25\right)=38$$

To find the opposite of 4x^{2}-25, find the opposite of each term.

$$4x^{2}+12x+9-4x^{2}+25=38$$

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

$$12x+9+25=38$$

Add 9 and 25 to get 34.

$$12x+34=38$$

Subtract 34 from both sides.

$$12x=38-34$$

Subtract 34 from 38 to get 4.

$$12x=4$$

Divide both sides by 12.

$$x=\frac{4}{12}$$

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

$$x=\frac{1}{3}$$