Solve (2y-3)*(3y+1)+2*(y-5)*(y+5)=2*left(1-2yright)^2+6y

$$(2y-3) \times (3y+1)+2 \times (y-5) \times (y+5)=2 \times { \left(1-2y \right) }^{ 2 } +6y$$

Solve for y

$$y=-11$$

Steps for Solving Linear Equation

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

$$6y^{2}-7y-3+2\left(y-5\right)\left(y+5\right)=2\left(1-2y\right)^{2}+6y$$

Use the distributive property to multiply 2 by y-5.

$$6y^{2}-7y-3+\left(2y-10\right)\left(y+5\right)=2\left(1-2y\right)^{2}+6y$$

Use the distributive property to multiply 2y-10 by y+5 and combine like terms.

$$6y^{2}-7y-3+2y^{2}-50=2\left(1-2y\right)^{2}+6y$$

Combine 6y^{2} and 2y^{2} to get 8y^{2}.

$$8y^{2}-7y-3-50=2\left(1-2y\right)^{2}+6y$$

Subtract 50 from -3 to get -53.

$$8y^{2}-7y-53=2\left(1-2y\right)^{2}+6y$$

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

$$8y^{2}-7y-53=2\left(1-4y+4y^{2}\right)+6y$$

Use the distributive property to multiply 2 by 1-4y+4y^{2}.

$$8y^{2}-7y-53=2-8y+8y^{2}+6y$$

Combine -8y and 6y to get -2y.

$$8y^{2}-7y-53=2-2y+8y^{2}$$

Add 2y to both sides.

$$8y^{2}-7y-53+2y=2+8y^{2}$$

Combine -7y and 2y to get -5y.

$$8y^{2}-5y-53=2+8y^{2}$$

Subtract 8y^{2} from both sides.

$$8y^{2}-5y-53-8y^{2}=2$$

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

$$-5y-53=2$$

Add 53 to both sides.

$$-5y=2+53$$

Add 2 and 53 to get 55.

$$-5y=55$$

Divide both sides by -5.

$$y=\frac{55}{-5}$$

Divide 55 by -5 to get -11.

$$y=-11$$