(x^2-4x) ^2+8x^2-32x+15=0

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To solve this quadratic equation, we need to expand the expression and simplify:

(x^2 - 4x)^2 + 8x^2 - 32x + 15 = 0
(x^4 - 8x^3 + 16x^2) + 8x^2 - 32x + 15 = 0
x^4 - 8x^3 + 16x^2 + 8x^2 - 32x + 15 = 0
x^4 - 8x^3 + 24x^2 - 32x + 15 = 0

This is now a quartic equation. Let's try to factorize or solve it using a numerical method like Newton-Raphson if it cannot be factored easily.