What are the solutions to the equation 6y^2+9y=15y^3 ?

The solutions to the equation 6y^2+9y=15y^3 are y=0,y=-3/5 ,y=1

Find the zeros of 6y^2+9y=15y^3

The zeros of 6y^2+9y=15y^3 are y=0,y=-3/5 ,y=1

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6 y^{2} + 9 y = 15 y^{3}

y = 0, y = - \frac{3}{5}, y = 1

Solution steps

6 y^{2} + 9 y = 15 y^{3}

Switch sides

15 y^{3} = 6 y^{2} + 9 y

Move

9 y

to the left side

15 y^{3} - 9 y = 6 y^{2}

Move

6 y^{2}

to the left side

15 y^{3} - 9 y - 6 y^{2} = 0

Factor

15 y^{3} - 9 y - 6 y^{2} : 3 y (5 y + 3) (y - 1)

3 y (5 y + 3) (y - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y = 0 or 5 y + 3 = 0 or y - 1 = 0

Solve

5 y + 3 = 0 : y = - \frac{3}{5}

Solve

y - 1 = 0 : y = 1

The solutions are

y = 0, y = - \frac{3}{5}, y = 1

x^{3} + 3 x^{2} - 4 x + 12 = 0

5 x^{3} + 30 x^{2} + 45 = 0

12 x^{3} + 24 x^{2} = 0

m^{3} + 3 m^{2} = 0

2 x^{3} - 9 x + 8 = 0

What are the solutions to the equation 6y^2+9y=15y^3 ?
The solutions to the equation 6y^2+9y=15y^3 are y=0,y=-3/5 ,y=1
Find the zeros of 6y^2+9y=15y^3
The zeros of 6y^2+9y=15y^3 are y=0,y=-3/5 ,y=1