Solve R=(4x^2-1)-(2x+1)(2x+3)

$$R = ( 4 x ^ { 2 } - 1 ) - ( 2 x + 1 ) ( 2 x + 3 )$$

Solve for R

$$R=-8x-4$$

Solution Steps

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

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

To find the opposite of 4x^{2}+8x+3, find the opposite of each term.

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

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

$$R=-1-8x-3$$

Subtract 3 from -1 to get -4.

$$R=-4-8x$$

Solve for x

$$x=-\frac{R}{8}-\frac{1}{2}$$

Steps for Solving Linear Equation

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

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

To find the opposite of 4x^{2}+8x+3, find the opposite of each term.

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

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

$$R=-1-8x-3$$

Subtract 3 from -1 to get -4.

$$R=-4-8x$$

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

$$-4-8x=R$$

Add 4 to both sides.

$$-8x=R+4$$

Divide both sides by -8.

$$\frac{-8x}{-8}=\frac{R+4}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$x=\frac{R+4}{-8}$$

Divide R+4 by -8.

$$x=-\frac{R}{8}-\frac{1}{2}$$