What are the solutions to the equation 6x^3=11x^2+10x ?

The solutions to the equation 6x^3=11x^2+10x are x=0,x=-2/3 ,x= 5/2

Find the zeros of 6x^3=11x^2+10x

The zeros of 6x^3=11x^2+10x are x=0,x=-2/3 ,x= 5/2

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6 x^{3} = 11 x^{2} + 10 x

x = 0, x = - \frac{2}{3}, x = \frac{5}{2}

Decimal Notation

x = 0, x = - 0.66666 \dots, x = 2.5

Solution steps

6 x^{3} = 11 x^{2} + 10 x

Move

10 x

to the left side

6 x^{3} - 10 x = 11 x^{2}

Move

11 x^{2}

to the left side

6 x^{3} - 10 x - 11 x^{2} = 0

Factor

6 x^{3} - 10 x - 11 x^{2} : x (3 x + 2) (2 x - 5)

x (3 x + 2) (2 x - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 x + 2 = 0 or 2 x - 5 = 0

Solve

3 x + 2 = 0 : x = - \frac{2}{3}

Solve

2 x - 5 = 0 : x = \frac{5}{2}

The solutions are

x = 0, x = - \frac{2}{3}, x = \frac{5}{2}

x^{4} - 6 x^{3} + 9 x^{2} = 0

x^{4} + 2 x^{2} = 0

4 x^{3} + 5 x^{2} + 36 x + 45 = 0

- h^{3} - 4 = 13

x^{5} + x = 1

What are the solutions to the equation 6x^3=11x^2+10x ?
The solutions to the equation 6x^3=11x^2+10x are x=0,x=-2/3 ,x= 5/2
Find the zeros of 6x^3=11x^2+10x
The zeros of 6x^3=11x^2+10x are x=0,x=-2/3 ,x= 5/2