Answer:

Step-by-step explanation:

10X^2 + 15x-34x -51
5x (2x+3)-17(2x+3)
(5x-17) (2x+3)
If your equation is ...

then it has no real solutions, and certainly no integer solutions.
_____
The attached graph show the left side is never equal to the right side of this equation for any real values of t.
Answer:150 possible different outcomes
Step-by-step explanation:
The number or colors from which we can choose is three, the number of letters five and the number of digits ten. And since we need to choose one each time. Is like finding the number of triples in the Cartesian set C x L x D, where C stands for colors, L for letters and D for digits, and all are finite sets. Then the number of elements in C x L x D is the product of the number of elements in each set, that is
|C x D x L|=|C|•|D|•|L|=3*5*10=150 different triplets or equivalently different outcomes.