Решение:

(x+12)^2 = x(x+8)

(x+12)(x+12) = x(x+8)

Expanding both sides:

x^2 + 24x + 144 = x^2 + 8x

Subtracting x^2 from both sides:

24x + 144 = 8x

Subtracting 8x from both sides:

16x + 144 = 0

Subtracting 144 from both sides:

16x = -144

Dividing by 16:

x = -9

Поэтому, значение x, при котором (x+12)^2 = x(x+8) равно -9.