By inspection, I see that x = -1 is one solution. Therefore x+1 is a factor.
Divide 2x^3 + 9x^2 +10x +3 by x-1 to get the other factor, a quadratic polynomial.
You should get 2x^2 + 7x + 3, using polynomial long division.
Now set that equal to zero and solve it for the other roots.
It factors easily to (2x+1)(x+3) = 0
The other two roots are x = -1/2 and x = -3
Solve for x:
2x^3 + 9x^2 +10x +3 =0
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