(x^2-4x+1)(x^2-4x+2)=12

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

(x^2-4x+1)(x^2-4x+2) = x^4 - 4x^3 + 2x^2 - 4x^3 + 16x^2 - 8x + x^2 - 4x + 2

Combining like terms, we get:

x^4 - 8x^3 + 19x^2 - 16x + 2 = 12

Now, we can simplify the equation by subtracting 12 from both sides:

x^4 - 8x^3 + 19x^2 - 16x - 10 = 0

This is a quartic equation that can be solved using various methods such as factoring, graphing, or numerical methods.