6y2-5y-6=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=6⋅-6=-36 and whose sum is b=-5.

Factor -5 out of -5y.

6y2-5y-6=0

Rewrite -5 as 4 plus -9

6y2+(4-9)y-6=0

Apply the distributive property.

6y2+4y-9y-6=0

6y2+4y-9y-6=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(6y2+4y)-9y-6=0

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

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

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

Factor the polynomial by factoring out the greatest common factor, 3y+2.

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

(3y+2)(2y-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.

3y+2=0

2y-3=0

Set the first factor equal to 0.

3y+2=0

Subtract 2 from both sides of the equation.

3y=-2

Divide each term by 3 and simplify.

Divide each term in 3y=-2 by 3.

3y3=-23

Cancel the common factor of 3.

Cancel the common factor.

3y3=-23

Divide y by 1.

y=-23

y=-23

Move the negative in front of the fraction.

y=-23

y=-23

y=-23

Set the next factor equal to 0.

2y-3=0

Add 3 to both sides of the equation.

2y=3

Divide each term by 2 and simplify.

Divide each term in 2y=3 by 2.

2y2=32

Cancel the common factor of 2.

Cancel the common factor.

2y2=32

Divide y by 1.

y=32

y=32

y=32

y=32

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

y=-23,32

Solve using the Square Root Property 6y^2-5y-6=0