What are the solutions to the equation 6x=(-2x)^3 ?

The solutions to the equation 6x=(-2x)^3 are x=0,x=(sqrt(3))/2 i,x=-(sqrt(3))/2 i

Find the zeros of 6x=(-2x)^3

The zeros of 6x=(-2x)^3 are x=0,x=(sqrt(3))/2 i,x=-(sqrt(3))/2 i

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6 x = (- 2 x)^{3}

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

Solution steps

6 x = (- 2 x)^{3}

Expand

(- 2 x)^{3} : - 8 x^{3}

6 x = - 8 x^{3}

Switch sides

- 8 x^{3} = 6 x

Move

6 x

to the left side

- 8 x^{3} - 6 x = 0

Factor

- 8 x^{3} - 6 x : - 2 x (4 x^{2} + 3)

- 2 x (4 x^{2} + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 4 x^{2} + 3 = 0

Solve

4 x^{2} + 3 = 0 : x = \frac{3}{2} i, x = - \frac{3}{2} i

The solutions are

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

10 x - 8 x^{2} - 2 x^{3} = 0

3 x^{4} - 48 = 0

x^{3} - 7 x^{2} + 3 x + 35 = 0

64 = a^{3}

m^{4} + 4 m^{2} - 12 = 0

What are the solutions to the equation 6x=(-2x)^3 ?
The solutions to the equation 6x=(-2x)^3 are x=0,x=(sqrt(3))/2 i,x=-(sqrt(3))/2 i
Find the zeros of 6x=(-2x)^3
The zeros of 6x=(-2x)^3 are x=0,x=(sqrt(3))/2 i,x=-(sqrt(3))/2 i