Pūraṇāpūraṇābhyāṃ

The Sutra means, by completion, or non-completion. It is a technique used to factorize and solve quadratic, cubic and bi-quadratic equations.

Let us assume (x+2)³:
(x + 2)³ = x³ + 6x² + 12x + 8

Clearly, the deficient terms are: (x + 2)

Adding (x+2) both sides:
(x³ + 6x² + 11x + 6) + (x + 2) = 0 + (x + 2)
or, (x + 2)³ = (x + 2)

Let, y = (x + 2). Then,
y³ = y solves for 0, 1 and -1

x + 2 = 0 gives: x = -2
Also, x + 2 = 1 gives: x = -1
And, x + 2 = -1 gives: x = -3

Thus, we get:
x = -2, x = -1, x = -3