-2y=5y2-7

Subtract 5y2 from both sides of the equation.

-2y-5y2=-7

Move 7 to the left side of the equation by adding it to both sides.

-2y-5y2+7=0

Let u=y. Substitute u for all occurrences of y.

-2u-5u2+7

Factor by grouping.

Reorder terms.

-5u2-2u+7

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=-5⋅7=-35 and whose sum is b=-2.

Factor -2 out of -2u.

-5u2-2(u)+7

Rewrite -2 as 5 plus -7

-5u2+(5-7)u+7

Apply the distributive property.

-5u2+5u-7u+7

-5u2+5u-7u+7

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(-5u2+5u)-7u+7

Factor out the greatest common factor (GCF) from each group.

5u(-u+1)+7(-u+1)

5u(-u+1)+7(-u+1)

Factor the polynomial by factoring out the greatest common factor, -u+1.

(-u+1)(5u+7)

(-u+1)(5u+7)

Replace all occurrences of u with y.

(-y+1)(5y+7)

Replace the left side with the factored expression.

(-y+1)(5y+7)=0

(-y+1)(5y+7)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

-y+1=0

5y+7=0

Set the first factor equal to 0.

-y+1=0

Subtract 1 from both sides of the equation.

-y=-1

Multiply each term in -y=-1 by -1

Multiply each term in -y=-1 by -1.

(-y)⋅-1=(-1)⋅-1

Multiply (-y)⋅-1.

Multiply -1 by -1.

1y=(-1)⋅-1

Multiply y by 1.

y=(-1)⋅-1

y=(-1)⋅-1

Multiply -1 by -1.

y=1

y=1

y=1

Set the next factor equal to 0.

5y+7=0

Subtract 7 from both sides of the equation.

5y=-7

Divide each term by 5 and simplify.

Divide each term in 5y=-7 by 5.

5y5=-75

Cancel the common factor of 5.

Cancel the common factor.

5y5=-75

Divide y by 1.

y=-75

y=-75

Move the negative in front of the fraction.

y=-75

y=-75

y=-75

The final solution is all the values that make (-y+1)(5y+7)=0 true.

y=1,-75

Solve using the Square Root Property -2y=5y^2-7