What are the solutions to the equation -x^3+6x^2-8x=-x^2+4x ?

The solutions to the equation -x^3+6x^2-8x=-x^2+4x are x=0,x=3,x=4

Find the zeros of -x^3+6x^2-8x=-x^2+4x

The zeros of -x^3+6x^2-8x=-x^2+4x are x=0,x=3,x=4

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- x^{3} + 6 x^{2} - 8 x = - x^{2} + 4 x

x = 0, x = 3, x = 4

Solution steps

- x^{3} + 6 x^{2} - 8 x = - x^{2} + 4 x

Move

4 x

to the left side

- x^{3} + 6 x^{2} - 12 x = - x^{2}

Move

x^{2}

to the left side

- x^{3} + 7 x^{2} - 12 x = 0

Factor

- x^{3} + 7 x^{2} - 12 x : - x (x - 3) (x - 4)

- x (x - 3) (x - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 3 = 0 or x - 4 = 0

Solve

x - 3 = 0 : x = 3

Solve

x - 4 = 0 : x = 4

The solutions are

x = 0, x = 3, x = 4

x^{3} + 4 x^{2} - 5 x + 12 = 0

0 = 2 x^{3} + 7 x^{2} - 21 x - 54

39 = x^{5} + x + 5

z^{3} = \frac{1}{8} i

49 x^{4} - 25 x^{2} = 0

What are the solutions to the equation -x^3+6x^2-8x=-x^2+4x ?
The solutions to the equation -x^3+6x^2-8x=-x^2+4x are x=0,x=3,x=4
Find the zeros of -x^3+6x^2-8x=-x^2+4x
The zeros of -x^3+6x^2-8x=-x^2+4x are x=0,x=3,x=4