Use factoring by grouping to solve the equation.

3x^{3} – x^{2} – 108x + 36 = 0

**Solution:-**

Notice that the expression on the left side of the equation can be grouped and factored.

Group the first two terms and the second two terms of 3x^{3} – x^{2} – 108x + 36. What is the missing expression?

3x^{3} – x^{2} – 108x + 36 = 0

(3x^{3} – x^{2}) = (108x – 36) = 0

Factor out x^{2} form the first grouping and 35 from the second. What is the remaining factor?

x^{2 }(3x – 1) – 36(x- 1) = 0

This reveals the common factor (3x – 1).

x^{2 }(3x – 1) – 36(x- 1) = 0

(x^{2} -36)(3x-1) = 0

Factor complete the left side of the equation. What are the missing factors?

(x- 6) (x + 6) (3x – 1) = 0

Now , use the zero product property to solve the equation. What are the solutions?

x – 6 = 0 or x + 6 = 0 or 3x – 1 = 0

x = 6 , -6 ,

The solution are x = 6 , -6 ,