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

The solutions to the equation x^2-6x=2x^2x are x=0,x= 1/4+i(sqrt(47))/4 ,x= 1/4-i(sqrt(47))/4

Find the zeros of x^2-6x=2x^2x

The zeros of x^2-6x=2x^2x are x=0,x= 1/4+i(sqrt(47))/4 ,x= 1/4-i(sqrt(47))/4

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x^{2} - 6 x = 2 x^{2} x

x = 0, x = \frac{1}{4} + i \frac{47}{4}, x = \frac{1}{4} - i \frac{47}{4}

Solution steps

x^{2} - 6 x = 2 x^{2} x

Switch sides

2 x^{2} x = x^{2} - 6 x

Move

6 x

to the left side

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

Move

x^{2}

to the left side

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

Factor

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

x (2 x^{2} - x + 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 2 x^{2} - x + 6 = 0

Solve

2 x^{2} - x + 6 = 0 : x = \frac{1}{4} + i \frac{47}{4}, x = \frac{1}{4} - i \frac{47}{4}

The solutions are

x = 0, x = \frac{1}{4} + i \frac{47}{4}, x = \frac{1}{4} - i \frac{47}{4}

- a^{3} + 6 a^{2} + 15 a + 8 = 0

3 = n^{3} - 3 n^{2} + n

n^{2} + n^{3} = - 180

x^{3} - 27 x - 27 = 0

x^{3} + 5 x^{2} + 6 x = - 30

What are the solutions to the equation x^2-6x=2x^2x ?
The solutions to the equation x^2-6x=2x^2x are x=0,x= 1/4+i(sqrt(47))/4 ,x= 1/4-i(sqrt(47))/4
Find the zeros of x^2-6x=2x^2x
The zeros of x^2-6x=2x^2x are x=0,x= 1/4+i(sqrt(47))/4 ,x= 1/4-i(sqrt(47))/4