To solve the equation (x^2 - 4)(2x + 10) = 0, we can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.

So, we set each factor equal to zero and solve for x:

First factor: x^2 - 4 = 0
Adding 4 to both sides: x^2 = 4
Taking the square root of both sides: x = ±2

Second factor: 2x + 10 = 0
Subtracting 10 from both sides: 2x = -10
Dividing both sides by 2: x = -5

Therefore, the solutions to the equation (x^2 - 4)(2x + 10) = 0 are x = -5, x = 2, and x = -2.