To solve the equation (x^2-4)(2x+x+3)=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.

First, let's simplify the equation:

(x^2-4)(2x+x+3) = 0

(x^2-4)(3x+3) = 0

Now, we have two factors: (x^2-4) and (3x+3). To find the values of x that make the equation true, we set each factor equal to zero and solve for x.

Setting the first factor equal to zero:

x^2-4 = 0

(x-2)(x+2) = 0

Now, we have two equations:

x-2 = 0 or x+2 = 0

Solving for x in each equation:

x-2 = 0 --> x = 2

x+2 = 0 --> x = -2

Setting the second factor equal to zero:

3x+3 = 0

3x = -3

x = -1

Therefore, the solutions to the equation (x^2-4)(2x+x+3)=0 are x = 2, x = -2, and x = -1.