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^2x^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.
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.