Solve for y y(3y-2)=5

y(3y-2)=5
Simplify y(3y-2).
Simplify by multiplying through.
Apply the distributive property.
y(3y)+y⋅-2=5
Reorder.
Rewrite using the commutative property of multiplication.
3y⋅y+y⋅-2=5
Move -2 to the left of y.
3y⋅y-2⋅y=5
3y⋅y-2⋅y=5
3y⋅y-2⋅y=5
Multiply y by y by adding the exponents.
Move y.
3(y⋅y)-2⋅y=5
Multiply y by y.
3y2-2⋅y=5
3y2-2y=5
3y2-2y=5
Move 5 to the left side of the equation by subtracting it from both sides.
3y2-2y-5=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=3⋅-5=-15 and whose sum is b=-2.
Factor -2 out of -2y.
3y2-2y-5=0
Rewrite -2 as 3 plus -5
3y2+(3-5)y-5=0
Apply the distributive property.
3y2+3y-5y-5=0
3y2+3y-5y-5=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(3y2+3y)-5y-5=0
Factor out the greatest common factor (GCF) from each group.
3y(y+1)-5(y+1)=0
3y(y+1)-5(y+1)=0
Factor the polynomial by factoring out the greatest common factor, y+1.
(y+1)(3y-5)=0
(y+1)(3y-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
3y-5=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
y+1=0
Subtract 1 from both sides of the equation.
y=-1
y=-1
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
3y-5=0
Add 5 to both sides of the equation.
3y=5
Divide each term by 3 and simplify.
Divide each term in 3y=5 by 3.
3y3=53
Cancel the common factor of 3.
Cancel the common factor.
3y3=53
Divide y by 1.
y=53
y=53
y=53
y=53
The final solution is all the values that make (y+1)(3y-5)=0 true.
y=-1,53
The result can be shown in multiple forms.
Exact Form:
y=-1,53
Decimal Form:
y=-1,1.6‾
Mixed Number Form:
y=-1,123
Solve for y y(3y-2)=5

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