(x-4)(x-5)(x-6)(x-7)=24

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To solve this equation, we first expand the left side of the equation:

(x-4)(x-5)(x-6)(x-7) = 24

Expanding the left side of the equation:

(x^2 - 5x + 4x - 20)(x^2 - 7x - 6x + 42) = 24

Simplifying further:

(x^2 - x - 20)(x^2 - 13x + 42) = 24

Next, expand this expression:

x^4 - 13x^2 + 42x -x^3 + 13x - 42 -20x^2 + 260 + 840 = 0

Combining like terms, we get:

x^4 - x^3 - 33x^2 + 55x + 798 = 0

Since this equation is already in standard form, we can find the solutions by factoring, using the rational roots theorem, or using a graphing calculator.