y(3y-2)=5

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

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.

y+1=0

Subtract 1 from both sides of the equation.

y=-1

y=-1

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