Solve the equation (3x+2)(x-4)=0 enter the solution with the highest value.

Using completing the square:
(3x+2)(x-4)=0
3x^2 - 12x + 2x - 8 = 0
3x^2 - 10x = 8
3(x^2 - 10x/3) = 8
3((x - 10/6)^2 - (10/6)^2) = 8
3((x - 5/3)^2 - (5/3)^2) = 8
3((x - 5/3)^2 - 25/9) = 8
3(x - 5/3)^2 - 25/3 = 8
3(x - 5/3)^2 = 49/3
(x - 5/3)^2 = 49/9
x - 5/3 = ±√(49/9)
x - 5/3 = ±(7/3)
x = (5/3) ± (7/3)
x = 12/3, -2/3
x = max(12/3, -2/3) = 12/3
x = 4