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

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

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply -2 by 2x+1.

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

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

$$4x^{2}+4x+1-3\left(2x-1\right)\left(2x+1\right)=-8x^{2}+8x+6$$

Add 8x^{2} to both sides.

$$4x^{2}+4x+1-3\left(2x-1\right)\left(2x+1\right)+8x^{2}=8x+6$$

Subtract 8x from both sides.

$$4x^{2}+4x+1-3\left(2x-1\right)\left(2x+1\right)+8x^{2}-8x=6$$

Use the distributive property to multiply -3 by 2x-1.

$$4x^{2}+4x+1+\left(-6x+3\right)\left(2x+1\right)+8x^{2}-8x=6$$

Use the distributive property to multiply -6x+3 by 2x+1 and combine like terms.

$$4x^{2}+4x+1-12x^{2}+3+8x^{2}-8x=6$$

Combine 4x^{2} and -12x^{2} to get -8x^{2}.

$$-8x^{2}+4x+1+3+8x^{2}-8x=6$$

Add 1 and 3 to get 4.

$$-8x^{2}+4x+4+8x^{2}-8x=6$$

Combine -8x^{2} and 8x^{2} to get 0.

$$4x+4-8x=6$$

Combine 4x and -8x to get -4x.

$$-4x+4=6$$

Subtract 4 from both sides.

$$-4x=6-4$$

Subtract 4 from 6 to get 2.

$$-4x=2$$

Divide both sides by -4.

$$x=\frac{2}{-4}$$

Reduce the fraction \frac{2}{-4} to lowest terms by extracting and canceling out 2.

$$x=-\frac{1}{2}$$