Question 1184237

Determinar una raíz de la siguiente ecuación
de variable “x”: x2 + (3a  -  2b)x  -  6ab = 0
<pre>{{{matrix(1,3, x^2 + (3a - 2b)x - 6ab, "=", 0)}}}
Using the "ac" method, we determine whcih 2 factors, when multiplied, gives "ac," or - 6ab. 
Furthermore, the same 2 factors sum to "b", or 3a - 2b. These 2 factors are: + 3a and - 2b
Rewrite the equation, substituting + 3ax - 2bx for (3a - 2b)x, to get: {{{matrix(1,3, x^2 + 3ax - 2bx - 6ab, "=", 0)}}}
x(x + 3a) - 2b(x + 3a) = 0
(x - 2b)(x + 3a) = 0
x - 2b = 0          OR          x + 3a = 0 ----- Setting each factor equal to 0.
    {{{highlight_green(matrix(1,3, x, "=", 2b))}}}       OR              {{{highlight_green(matrix(1,3, x, "=", - 3a))}}}