+23246 If you can't do this by graphing, it's a painful process ...
If there are any rational solutions, the numerator is a divisor of 45:
1, -1, 3, -3, 5. -5. 9. -9. 15. -15. 45. -45
and the denominator is a divisor of 6:
1, -1, 2, -2, 3, -3, 6, -6
If you try enough of these, you'll find that both -5/3 and -3/2 are solutions.
This means that 3x + 5 and 2x + 3 are factors.
If you divide 6x4 + 49x3 128x2 + 132x + 45 by (3x + 5)(2x + 4)
you'll get the quotient x2 + 5x + 3.
Then, apply the quadratic formula to x2 + 5x + 3 to get the final two solutions.
