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

6y2-5y-6=0
Factor by grouping.
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 and solve.
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 and solve.
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