# Solve for y y(3y+2)=9

y(3y+2)=9
Simplify y(3y+2).
Simplify by multiplying through.
Apply the distributive property.
y(3y)+y⋅2=9
Reorder.
Rewrite using the commutative property of multiplication.
3y⋅y+y⋅2=9
Move 2 to the left of y.
3y⋅y+2⋅y=9
3y⋅y+2⋅y=9
3y⋅y+2⋅y=9
Multiply y by y by adding the exponents.
Move y.
3(y⋅y)+2⋅y=9
Multiply y by y.
3y2+2⋅y=9
3y2+2y=9
3y2+2y=9
Move 9 to the left side of the equation by subtracting it from both sides.
3y2+2y-9=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=3, b=2, and c=-9 into the quadratic formula and solve for y.
-2±22-4⋅(3⋅-9)2⋅3
Simplify.
Simplify the numerator.
Raise 2 to the power of 2.
y=-2±4-4⋅(3⋅-9)2⋅3
Multiply 3 by -9.
y=-2±4-4⋅-272⋅3
Multiply -4 by -27.
y=-2±4+1082⋅3
y=-2±1122⋅3
Rewrite 112 as 42⋅7.
Factor 16 out of 112.
y=-2±16(7)2⋅3
Rewrite 16 as 42.
y=-2±42⋅72⋅3
y=-2±42⋅72⋅3
Pull terms out from under the radical.
y=-2±472⋅3
y=-2±472⋅3
Multiply 2 by 3.
y=-2±476
Simplify -2±476.
y=-1±273
y=-1±273
The final answer is the combination of both solutions.
y=-1-273,-1+273
The result can be shown in multiple forms.
Exact Form:
y=-1-273,-1+273
Decimal Form:
y=1.43050087…,-2.09716754…
Solve for y y(3y+2)=9

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