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To solve this equation, we first need to simplify the left side by expanding the terms:

(a³ - 2a²) - (9a + 18) = 0

a³ - 2a² - 9a - 18 = 0

Next, we combine like terms:

a³ - 2a² - 9a - 18 = 0

Now, we can factor out an 'a' from the first two terms:

a(a² - 2a) - 9a - 18 = 0

Then, we can factor out a '-9' from the last two terms:

a(a² - 2a) - 9(a + 2) = 0

Now, we can factor out the common factor 'a' from the first two terms:

a(a - 2)(a) - 9(a + 2) = 0

(a - 2)(a²) - 9(a + 2) = 0

Now, we expand the terms again:

a³ - 2a² - 9a - 18 = 0

Now, we have a quadratic equation:

a³ - 2a² - 9a - 18 = 0

We can solve this equation by factoring, using the quadratic formula, or by using synthetic division. The solutions to this equation are the values of 'a' that make the equation true.