# Decide equation using only factors to solve this problem 12x^{2} + 5x - 2 = 0

Decide equation using only factors to solve this problem
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In order to factor the quadratic, we need to find the values of a, b and c for the given quadratic on comparing with standard quadratic

Now, let us apply ac method to factor the quadratic.
We got So, we need to find the factors of -24, those add upto 5.
(Product)
$b=5$(Sum)
-24 could be factored in two numbers 8 and -3 that add upto 5.
Therefore, middle term 5x of expression could be break into two terms 8x and -3x.
Then we need to make the break the expression into groups.
Factor out 3x form and factor out 2 from:

Then factor out common parenthesis
We got factored form

Factor out common parenthesis

By applying zero product rule, we need to set each factor equal to zero and solve for x.
We got

$+1+1-2-2$