-7y=2y2+5

Subtract 2y2 from both sides of the equation.

-7y-2y2=5

Move 5 to the left side of the equation by subtracting it from both sides.

-7y-2y2-5=0

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

-7u-2u2-5

Factor by grouping.

Reorder terms.

-2u2-7u-5

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=-2⋅-5=10 and whose sum is b=-7.

Factor -7 out of -7u.

-2u2-7(u)-5

Rewrite -7 as -2 plus -5

-2u2+(-2-5)u-5

Apply the distributive property.

-2u2-2u-5u-5

-2u2-2u-5u-5

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(-2u2-2u)-5u-5

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

2u(-u-1)+5(-u-1)

2u(-u-1)+5(-u-1)

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

(-u-1)(2u+5)

(-u-1)(2u+5)

Replace all occurrences of u with y.

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

Replace the left side with the factored expression.

(-y-1)(2y+5)=0

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

2y+5=0

Set the first factor equal to 0.

-y-1=0

Add 1 to 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.

2y+5=0

Subtract 5 from both sides of the equation.

2y=-5

Divide each term by 2 and simplify.

Divide each term in 2y=-5 by 2.

2y2=-52

Cancel the common factor of 2.

Cancel the common factor.

2y2=-52

Divide y by 1.

y=-52

y=-52

Move the negative in front of the fraction.

y=-52

y=-52

y=-52

The final solution is all the values that make (-y-1)(2y+5)=0 true.

y=-1,-52

The result can be shown in multiple forms.

Exact Form:

y=-1,-52

Decimal Form:

y=-1,-2.5

Mixed Number Form:

y=-1,-212

Solve for y -7y=2y^2+5