Solve (2y+1)(y-1)=(y+5)(2y-5)

$$(2y+1)(y-1)=(y+5)(2y-5)$$

Solve for y

$$y=4$$

Steps for Solving Linear Equation

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

$$2y^{2}-y-1=\left(y+5\right)\left(2y-5\right)$$

Use the distributive property to multiply y+5 by 2y-5 and combine like terms.

$$2y^{2}-y-1=2y^{2}+5y-25$$

Subtract 2y^{2} from both sides.

$$2y^{2}-y-1-2y^{2}=5y-25$$

Combine 2y^{2} and -2y^{2} to get 0.

$$-y-1=5y-25$$

Subtract 5y from both sides.

$$-y-1-5y=-25$$

Combine -y and -5y to get -6y.

$$-6y-1=-25$$

Add 1 to both sides.

$$-6y=-25+1$$

Add -25 and 1 to get -24.

$$-6y=-24$$

Divide both sides by -6.

$$y=\frac{-24}{-6}$$

Divide -24 by -6 to get 4.

$$y=4$$