9y2-y5=0

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.

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.

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