Find the real-number solutions of the equation

The step of finding the real-number solutions 2x^5 + 24x = 14x^3. Thanks

Bring the 14x^3 to the other side:
2x^5 - 14x^3 + 24x = 0

Factor out 2x:
2x(x^4 - 7x^2 + 12) = 0

Factor the contents of the parentheses in terms of x^2:
2x(x^2 - 4)(x^2 - 3) = 0

Note that x^2 - 4 = (x + 2)(x - 2)
Also that x^2 - 3 = (x + √3)(x - √3)

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

SOLUTION: Using the zero factor property, x = 0, -2, 2, -√3, √3

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