4x^2-36=0

To solve the quadratic equation 4x^2-36=0, we can first factor out the greatest common factor, which is 4:

4(x^2 - 9) = 0

We can further simplify the equation by factoring the difference of squares:

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

Now, we can apply 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 zero:

Setting each factor equal to zero, we have:

x - 3 = 0 or x + 3 = 0

Solving for x in each equation:

x = 3 or x = -3

So, the solutions to the equation 4x^2-36=0 are x = 3 and x = -3.