To solve this equation, we need to isolate x on one side of the equation.

Starting with the given equation:

-4x^2 + 16 = 0

First, subtract 16 from both sides of the equation to get:

-4x^2 = -16

Next, divide both sides by -4 to solve for x:

x^2 = 4

Now, take the square root of both sides to solve for x:

x = ±2

Therefore, the solutions to the equation -4x^2 + 16 = 0 are x = 2 and x = -2.