What are the solutions to the equation 3(4g^6)=2(6g^9) ?

The solutions to the equation 3(4g^6)=2(6g^9) are g=0,g=1,g=-1/2+i(sqrt(3))/2 ,g=-1/2-i(sqrt(3))/2

Find the zeros of 3(4g^6)=2(6g^9)

The zeros of 3(4g^6)=2(6g^9) are g=0,g=1,g=-1/2+i(sqrt(3))/2 ,g=-1/2-i(sqrt(3))/2

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3 (4 g^{6}) = 2 (6 g^{9})

g = 0, g = 1, g = - \frac{1}{2} + i \frac{3}{2}, g = - \frac{1}{2} - i \frac{3}{2}

Solution steps

3 (4 g^{6}) = 2 (6 g^{9})

Move

2 (6 g^{9})

to the left side

3 \cdot 4 g^{6} - 2 \cdot 6 g^{9} = 0

Factor

3 \cdot 4 g^{6} - 2 \cdot 6 g^{9} : - 12 g^{6} (g - 1) (g^{2} + g + 1)

- 12 g^{6} (g - 1) (g^{2} + g + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

g = 0 or g - 1 = 0 or g^{2} + g + 1 = 0

Solve

g - 1 = 0 : g = 1

Solve

g^{2} + g + 1 = 0 : g = - \frac{1}{2} + i \frac{3}{2}, g = - \frac{1}{2} - i \frac{3}{2}

The solutions are

g = 0, g = 1, g = - \frac{1}{2} + i \frac{3}{2}, g = - \frac{1}{2} - i \frac{3}{2}

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

2 x^{4} - 7 x^{2} = 4

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

x^{11} + \frac{2}{9} x = 32

x^{4} + 32 x^{2} + 256 = 0

What are the solutions to the equation 3(4g^6)=2(6g^9) ?
The solutions to the equation 3(4g^6)=2(6g^9) are g=0,g=1,g=-1/2+i(sqrt(3))/2 ,g=-1/2-i(sqrt(3))/2
Find the zeros of 3(4g^6)=2(6g^9)
The zeros of 3(4g^6)=2(6g^9) are g=0,g=1,g=-1/2+i(sqrt(3))/2 ,g=-1/2-i(sqrt(3))/2