What are the solutions to the equation 2x^3-3x^2-9x=x^3-2x^2-3x ?

The solutions to the equation 2x^3-3x^2-9x=x^3-2x^2-3x are x=0,x=-2,x=3

Find the zeros of 2x^3-3x^2-9x=x^3-2x^2-3x

The zeros of 2x^3-3x^2-9x=x^3-2x^2-3x are x=0,x=-2,x=3

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2 x^{3} - 3 x^{2} - 9 x = x^{3} - 2 x^{2} - 3 x

x = 0, x = - 2, x = 3

Solution steps

2 x^{3} - 3 x^{2} - 9 x = x^{3} - 2 x^{2} - 3 x

Subtract

x^{3} - 2 x^{2} - 3 x

from both sides

2 x^{3} - 3 x^{2} - 9 x - (x^{3} - 2 x^{2} - 3 x) = x^{3} - 2 x^{2} - 3 x - (x^{3} - 2 x^{2} - 3 x)

Simplify

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

Factor

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

x (x + 2) (x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 2 = 0 or x - 3 = 0

Solve

x + 2 = 0 : x = - 2

Solve

x - 3 = 0 : x = 3

The solutions are

x = 0, x = - 2, x = 3

6 x + 12 = 3 x^{3}

- 5 x^{5} + 5 x = 0

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

x^{8} = - 256

x^{4} - 4 x^{3} + 4 x^{2}

What are the solutions to the equation 2x^3-3x^2-9x=x^3-2x^2-3x ?
The solutions to the equation 2x^3-3x^2-9x=x^3-2x^2-3x are x=0,x=-2,x=3
Find the zeros of 2x^3-3x^2-9x=x^3-2x^2-3x
The zeros of 2x^3-3x^2-9x=x^3-2x^2-3x are x=0,x=-2,x=3