# Solve for y 2y^2-3=5y 2y2-3=5y
Subtract 5y from both sides of the equation.
2y2-3-5y=0
Factor by grouping.
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 and solve.
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 and solve.
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
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