(x-4)(x+3)(x-6)(x+2)=10x^2

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вопрос

Before solving this equation, we need to expand the left side of the equation by multiplying the factors together.

(x-4)(x+3)(x-6)(x+2) = (x^2 - 4x + 3x - 12)(x^2 - 6x + 2x - 12)
= (x^2 - x - 12)(x^2 - 4x - 12)
= x^4 - 4x^2 - 12x - x^3 + 4x + 12
= x^4 - x^3 - 4x^2 + 16x - 12

Now, we can set this expression equal to 10x^2:

x^4 - x^3 - 4x^2 + 16x - 12 = 10x^2
x^4 - x^3 - 14x^2 + 16x - 12 = 0

This is a quartic equation that can be solved by factoring, but it may be quite complex. One possible approach is to simplify the equation further and then try to factor it.