I understand problems like this but with just a variable in the first one. Here, it has 12. This throws me off.
factor 12m^2 + 25m + 12 = 0.
If you can't quickly factor the equation, it is generally easier to just use the quadratic equation. As you do more and more, you will probably remember how you factored them previously.
m=-3/4
m=-4/3
easier to figure out the roots using the quadratic formula.
{-b+\-[sqrt(b2-4ac)]}/2a
(I hope you are aware of it). Before going and manually solving the eqn, its better to check if b2-4ac is positive or not.(if -ve, equation has imaginary roots).
divide the expression by 12 first and then use the formula..
To solve the quadratic equation 12m^2 + 25m + 12 = 0, we need to factor it.
First, let's identify two numbers whose product is 12 (the coefficient of m^2 term) and whose sum is 25 (the coefficient of the m term). These numbers are 3 and 4, since 3 * 4 = 12 and 3 + 4 = 7.
Now, we rewrite the middle term (25m) as the sum of these two numbers: 3m + 4m. The equation becomes:
12m^2 + 3m + 4m + 12 = 0.
Next, we group the terms:
(12m^2 + 3m) + (4m + 12) = 0.
Now, let's factor out the greatest common factor from each group:
3m(4m + 1) + 4(4m + 1) = 0.
Notice that we have a common binomial factor, (4m + 1), which is present in both terms. Hence, we can factor it out:
(4m + 1)(3m + 4) = 0.
Now, we set each factor equal to zero and solve for m:
4m + 1 = 0 --> 4m = -1 --> m = -1/4.
3m + 4 = 0 --> 3m = -4 --> m = -4/3.
Therefore, the solutions for the equation 12m^2 + 25m + 12 = 0 are m = -1/4 and m = -4/3.