Solve (x+2)(x-2)+3x^2=(2x+1)^2+2x

$$( x + 2 ) ( x - 2 ) + 3 x ^ { 2 } = ( 2 x + 1 ) ^ { 2 } + 2 x$$

Solve for x

$$x=-\frac{5}{6}\approx -0.833333333$$

Steps for Solving Linear Equation

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.

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

Combine x^{2} and 3x^{2} to get 4x^{2}.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.

$$4x^{2}-4=4x^{2}+4x+1+2x$$

Combine 4x and 2x to get 6x.

$$4x^{2}-4=4x^{2}+6x+1$$

Subtract 4x^{2} from both sides.

$$4x^{2}-4-4x^{2}=6x+1$$

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

$$-4=6x+1$$

Swap sides so that all variable terms are on the left hand side.

$$6x+1=-4$$

Subtract 1 from both sides.

$$6x=-4-1$$

Subtract 1 from -4 to get -5.

$$6x=-5$$

Divide both sides by 6.

$$x=\frac{-5}{6}$$

Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$x=-\frac{5}{6}$$