solve the equation .
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2x³ - 3x² - 11x + 6 = 0

First find a root by inspection:

P(x) = 2x³ - 3x² - 11x + 6

P(-2) = -16 -12 + 22 + 6 = 0 so (x + 2) is a factor of P(x)

Then after doing synthetic division:

2x² - 7x + 3 is found as a quadratic factor of P(x)

Factoring the quadratic:

(2x - 1)(x - 3)

So (x + 2)(2x - 1)(x - 3) = 0

x + 2 = 0 or 2x - 1 = 0 or x - 3 = 0

x = -2 or x = 1/2 or x = 3

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