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Solution:
Given equation is 2x2 + 8x = x2 - 16
We can write it as 2x2 - x2 + 8x + 16 = 0
=> x2 + 8x + 16 = 0
This is a quadratic equation in x
x2 + 4x + 4x + 16 = 0
x(x + 4) + 4(x + 4) = 0
(x + 4)(x + 4) = 0
x = -4, -4
Therefore, the solution for the given equation is -4, -4.
Summary:
The only solution of 2x2 + 8x = x2 - 16 is -4.