solve for 8m^2 +20m=12 for m by factoring

divide by 4 first

2 m^2 + 5 m - 3 = 0

(2m-1)(m+3) = 0

m = 1/2 or -3

8m^2 +20m=12

8m^2 +20m-12=0

divide each term by 4

2m^2 + 5m - 3 = 0
(2m - 1)(n + 3) = 0

m = 1/2 or m = -3

To solve the equation 8m^2 + 20m = 12 by factoring, we need to rearrange the equation to equal to zero:

8m^2 + 20m - 12 = 0

To factor the equation, we can break down the middle term into two terms that when multiplied together give the product of the coefficient of the first term (8) and the constant term (-12). In this case, the product is -96.

We need to find two numbers whose product is -96 and whose sum is the coefficient of the middle term (20). After analyzing the factors of -96, we find that the numbers are 24 and -4.

Now we can rewrite the middle term:

8m^2 + 24m - 4m - 12 = 0

Next, factor by grouping:

(8m^2 + 24m) - (4m + 12) = 0

Taking out the greatest common factor (8m) from the first group and (4) from the second group:

8m(m + 3) - 4(m + 3) = 0

Now, we have a common binomial factor (m + 3) in both terms:

(8m - 4)(m + 3) = 0

Now, set each factor equal to zero and solve for m:

8m - 4 = 0 or m + 3 = 0

Solving for m in the first equation:

8m - 4 = 0
8m = 4
m = 4/8
m = 1/2

Solving for m in the second equation:

m + 3 = 0
m = -3

So the two solutions for the equation 8m^2 + 20m = 12 by factoring are m = 1/2 and m = -3.

To solve the equation 8m^2 + 20m = 12 by factoring, we first rearrange the equation to set it equal to zero:

8m^2 + 20m - 12 = 0

Next, we look for common factors that can be factored out of each term. In this case, we can divide each term by 4:

4(2m^2 + 5m - 3) = 0

Now, we need to factor the quadratic expression (2m^2 + 5m - 3). To do this, we look for two numbers that multiply to give -6 and add up to 5. These numbers are 6 and -1:

4(2m^2 + 6m - m - 3) = 0

Now, we group the terms and factor by grouping:

4(2m(m + 3) - 1(m + 3)) = 0

Notice that there is a common binomial factor of (m + 3), so we can factor that out:

4(m + 3)(2m - 1) = 0

Finally, we can set each factor equal to zero to solve for m:

m + 3 = 0 or 2m - 1 = 0

Solving each equation separately:

For m + 3 = 0:
m = -3

For 2m - 1 = 0:
2m = 1
m = 1/2

Therefore, the solutions to the equation 8m^2 + 20m = 12 are m = -3 and m = 1/2.