Factorise: 45x (x - 2)²+60x(x - 2)+20x

An equation is in the form of ax² + bx + c = 0. To solve this equation we will use properties and factors.

Answer: 45x (x - 2)²+60x(x - 2)+20x can be factorized as 5x (3x - 4) (3x - 4)

Let us solve the equation for the value of x.

Explanation:

Given: 45 x (x - 2)² + 60 x (x - 2) + 20 x

Using (a - b)² = a² - 2 ab + b²

⇒ 45 x (x² - 4x + 4) + 60 x (x - 2) + 20 x = 0

⇒ 45 x³ - 180 x² + 180 x + 60 x² - 120 x + 20 x = 0

⇒ 45 x³ - 120 x² + 80 x = 0 

By splitting the middle term, we get

⇒ 45 x³ - 60 x² - 60 x² + 80 x = 0

By taking out common factors, we get

⇒ 15 x² (3x - 4) - 20x (3x - 4) = 0

⇒ (15 x² - 20 x) (3x - 4) = 0

⇒ 5x (3x - 4) (3x - 4) = 0

Thus, the factorization for 45 x (x - 2)² + 60 x (x - 2) + 20 x is 5x (3x - 4) (3x - 4).