Answer
$x=\frac{2}{3}~~$ or $~~x=-\frac{3}{2}$
Work Step by Step
Let's consider a trinomial in this form: $~ax^2+bx+c$
To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = a\times c$
Then the next step is to rewrite the trinomial as follows:
$~x^2+bx+c = ax^2+rx+sx+c$
We can rewrite the given equation and use the GCF to factor it:
$12x^2 +10x = 12$
$12x^2 +10x - 12 = 0$
$(2)~(6x^2 +5x - 6) = 0$
To factor the left side of this equation, we need to find two numbers $r$ and $s$ such that $r+s = 5~$ and $~r\times s = -36$. We can see that $(9)+(-4) = 5~$ and $(9)\times (-4) = -36$
We can solve the equation as follows:
$12x^2 +10x = 12$
$12x^2 +10x - 12 = 0$
$(2)~(6x^2 +5x - 6) = 0$
$(2)~(6x^2 +9x - 4x - 6) = 0$
$(2)~[~(6x^2 +9x)+(- 4x - 6)~] = 0$
$(2)~[~(3x)(2x +3)+(-2)(2x +3)~] = 0$
$(2)~(3x-2)~(2x +3) = 0$
$3x-2 = 0~~$ or $~~2x+3 = 0$
$x=\frac{2}{3}~~$ or $~~x=-\frac{3}{2}$
