Solve (2y-3)(3y+1)+2(y-5)(y+5)=2(7-2y)^2+6y

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

Solve for y

$$y = \frac{151}{43} = 3\frac{22}{43} \approx 3.511627907$$

Steps for Solving Linear Equation

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

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

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

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

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

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

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

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

Subtract 50 from -3 to get -53.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(7-2y\right)^{2}.

$$8y^{2}-7y-53=2\left(49-28y+4y^{2}\right)+6y$$

Use the distributive property to multiply 2 by 49-28y+4y^{2}.

$$8y^{2}-7y-53=98-56y+8y^{2}+6y$$

Combine -56y and 6y to get -50y.

$$8y^{2}-7y-53=98-50y+8y^{2}$$

Add 50y to both sides.

$$8y^{2}-7y-53+50y=98+8y^{2}$$

Combine -7y and 50y to get 43y.

$$8y^{2}+43y-53=98+8y^{2}$$

Subtract 8y^{2} from both sides.

$$8y^{2}+43y-53-8y^{2}=98$$

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

$$43y-53=98$$

Add 53 to both sides.

$$43y=98+53$$

Add 98 and 53 to get 151.

$$43y=151$$

Divide both sides by 43.

$$y=\frac{151}{43}$$