The given equation is
5x^2 + 12x + 4 = 0
This is a quadratic equation. We would solve by applying the method of factorisation. The first step is to multiply 5x^2 with 4. It becomes 20x^2. We would find two terms such that their sum or difference is 12x and their product is 20x^2. The terms are 10x and 2x. By replacing 12x with 10x + 2x, we have
5x^2 + 10x + 2x + 4 = 0
The next step is to factorise by grouping. The groups are (5x^2 + 12) and (2x + 4). It becomes
5x(x + 2) + 2(x + 2) = 0
Since x + 2 is common, it becomes
(x + 2)(5x + 2) = 0
x + 2 = 0 or 5x + 2 = 0
x = - 2 or 5x = - 2
x = - 2 or x = - 2/5