To solve the equation (x^2 + 1)(3x - 4) = 0, we can set each factor equal to zero and solve for x.

Setting x^2 + 1 = 0:
x^2 = -1
Taking the square root of both sides, we get:
x = ±√(-1)
Since the square root of a negative number is not a real number, there are no real solutions for this factor.

Setting 3x - 4 = 0:
3x = 4
Dividing both sides by 3, we get:
x = 4/3

Therefore, the only real solution to the equation (x^2 + 1)(3x - 4) = 0 is x = 4/3.