# Solve for y 9y^2-y^5=0

9y2-y5=0
Factor y2 out of 9y2-y5.
Factor y2 out of 9y2.
y2⋅9-y5=0
Factor y2 out of -y5.
y2⋅9+y2(-y3)=0
Factor y2 out of y2⋅9+y2(-y3).
y2(9-y3)=0
y2(9-y3)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
y2=0
9-y3=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
y2=0
Take the square root of both sides of the equation to eliminate the exponent on the left side.
y=±0
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite 0 as 02.
y=±02
Pull terms out from under the radical, assuming positive real numbers.
y=±0
y=±0
±0 is equal to 0.
y=0
y=0
y=0
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
9-y3=0
Subtract 9 from both sides of the equation.
-y3=-9
Move 9 to the left side of the equation by adding it to both sides.
-y3+9=0
Factor -1 out of -y3+9.
Factor -1 out of -y3.
-(y3)+9=0
Rewrite 9 as -1(-9).
-(y3)-1⋅-9=0
Factor -1 out of -(y3)-1(-9).
-(y3-9)=0
-(y3-9)=0
Multiply each term in -(y3-9)=0 by -1
Multiply each term in -(y3-9)=0 by -1.
-(y3-9)⋅-1=0⋅-1
Simplify -(y3-9)⋅-1.
Apply the distributive property.
(-y3–9)⋅-1=0⋅-1
Multiply -1 by -9.
(-y3+9)⋅-1=0⋅-1
Apply the distributive property.
-y3⋅-1+9⋅-1=0⋅-1
Multiply -y3⋅-1.
Multiply -1 by -1.
1y3+9⋅-1=0⋅-1
Multiply y3 by 1.
y3+9⋅-1=0⋅-1
y3+9⋅-1=0⋅-1
Multiply 9 by -1.
y3-9=0⋅-1
y3-9=0⋅-1
Multiply 0 by -1.
y3-9=0
y3-9=0
Add 9 to both sides of the equation.
y3=9
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
y=93
y=93
The final solution is all the values that make y2(9-y3)=0 true.
y=0,93
The result can be shown in multiple forms.
Exact Form:
y=0,93
Decimal Form:
y=0,2.08008382…
Solve for y 9y^2-y^5=0

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