To solve the equation 3√x + 3 + √x^2 - 9 = 0, we can start by simplifying the equation.

First, let's simplify the square root term: √x^2 = x.

Now, the equation becomes 3√x + 3 + x - 9 = 0.

Combining like terms, we have 4√x + x - 6 = 0.

Next, let's isolate the square root term by subtracting x from both sides: 4√x = -x + 6.

To eliminate the square root, we need to square both sides of the equation: (4√x)^2 = (-x + 6)^2.

Simplifying further, we get 16x = x^2 - 12x + 36.

Rearranging the equation, we have x^2 - 28x + 36 = 0.

Now, we can solve this quadratic equation by factoring or using the quadratic formula.

Factoring the equation, we have (x - 2)(x - 18) = 0.

Setting each factor equal to zero, we get x - 2 = 0 or x - 18 = 0.

Solving for x, we find x = 2 or x = 18.

Therefore, the solutions to the equation 3√x + 3 + √x^2 - 9 = 0 are x = 2 and x = 18.