What are the solutions to the equation 4x^3=16x^2-48x ?

The solutions to the equation 4x^3=16x^2-48x are x=0,x=2+2sqrt(2)i,x=2-2sqrt(2)i

Find the zeros of 4x^3=16x^2-48x

The zeros of 4x^3=16x^2-48x are x=0,x=2+2sqrt(2)i,x=2-2sqrt(2)i

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4 x^{3} = 16 x^{2} - 48 x

x = 0, x = 2 + 22 i, x = 2 - 22 i

Solution steps

4 x^{3} = 16 x^{2} - 48 x

Move

48 x

to the left side

4 x^{3} + 48 x = 16 x^{2}

Move

16 x^{2}

to the left side

4 x^{3} + 48 x - 16 x^{2} = 0

Factor

4 x^{3} + 48 x - 16 x^{2} : 4 x (x^{2} - 4 x + 12)

4 x (x^{2} - 4 x + 12) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x^{2} - 4 x + 12 = 0 : x = 2 + 22 i, x = 2 - 22 i

The solutions are

x = 0, x = 2 + 22 i, x = 2 - 22 i

- x^{3} + 8 x^{2} - 13 x + 2 = 0

r^{4} - r + 1 = 0

x^{3} - 5 x^{2} - 8 x = 12

z^{4} = - 2 - 23

10 x (x^{2} - 4)^{4} = 0

What are the solutions to the equation 4x^3=16x^2-48x ?
The solutions to the equation 4x^3=16x^2-48x are x=0,x=2+2sqrt(2)i,x=2-2sqrt(2)i
Find the zeros of 4x^3=16x^2-48x
The zeros of 4x^3=16x^2-48x are x=0,x=2+2sqrt(2)i,x=2-2sqrt(2)i