Solve (1-2y)^2=(2y-1)(2y+7)

$$( 1 - 2 y ) ^ { 2 } = ( 2 y - 1 ) ( 2 y + 7 )$$

Solve for y

$$y=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

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

$$1-4y+4y^{2}=\left(2y-1\right)\left(2y+7\right)$$

Use the distributive property to multiply 2y-1 by 2y+7 and combine like terms.

$$1-4y+4y^{2}=4y^{2}+12y-7$$

Subtract 4y^{2} from both sides.

$$1-4y+4y^{2}-4y^{2}=12y-7$$

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

$$1-4y=12y-7$$

Subtract 12y from both sides.

$$1-4y-12y=-7$$

Combine -4y and -12y to get -16y.

$$1-16y=-7$$

Subtract 1 from both sides.

$$-16y=-7-1$$

Subtract 1 from -7 to get -8.

$$-16y=-8$$

Divide both sides by -16.

$$y=\frac{-8}{-16}$$

Reduce the fraction \frac{-8}{-16} to lowest terms by extracting and canceling out -8.

$$y=\frac{1}{2}$$