2y2-3=5y

Subtract 5y from both sides of the equation.

2y2-3-5y=0

Reorder terms.

2y2-5y-3=0

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⋅-3=-6 and whose sum is b=-5.

Factor -5 out of -5y.

2y2-5y-3=0

Rewrite -5 as 1 plus -6

2y2+(1-6)y-3=0

Apply the distributive property.

2y2+1y-6y-3=0

Multiply y by 1.

2y2+y-6y-3=0

2y2+y-6y-3=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(2y2+y)-6y-3=0

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

y(2y+1)-3(2y+1)=0

y(2y+1)-3(2y+1)=0

Factor the polynomial by factoring out the greatest common factor, 2y+1.

(2y+1)(y-3)=0

(2y+1)(y-3)=0

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

2y+1=0

y-3=0

Set the first factor equal to 0.

2y+1=0

Subtract 1 from both sides of the equation.

2y=-1

Divide each term by 2 and simplify.

Divide each term in 2y=-1 by 2.

2y2=-12

Cancel the common factor of 2.

Cancel the common factor.

2y2=-12

Divide y by 1.

y=-12

y=-12

Move the negative in front of the fraction.

y=-12

y=-12

y=-12

Set the next factor equal to 0.

y-3=0

Add 3 to both sides of the equation.

y=3

y=3

The final solution is all the values that make (2y+1)(y-3)=0 true.

y=-12,3

The result can be shown in multiple forms.

Exact Form:

y=-12,3

Decimal Form:

y=-0.5,3

Solve for y 2y^2-3=5y