(x+6)^2 = (15-x)^2

(x+6)(x+6) = (15-x)(15-x)

Expanding both sides:

x^2 + 12x + 36 = 225 - 30x + x^2

Rearranging terms:

12x + 36 = 225 - 30x

Combining like terms:

12x + 30x = 225 - 36

42x = 189

Dividing by 42:

x = 189 / 42

x = 9/2 or x = 4.5

Therefore, the solutions to the equation are x = 9/2 or x = 4.5.