Sure, let's solve the equation step-by-step:
Given the equation:
[tex]\[
(2 m + 3)(4 m + 3) = 0
\][/tex]
We can use the property that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for \( m \).
1. First factor:
[tex]\[
2 m + 3 = 0
\][/tex]
Subtract 3 from both sides:
[tex]\[
2 m = -3
\][/tex]
Now, divide both sides by 2:
[tex]\[
m = -\frac{3}{2}
\][/tex]
2. Second factor:
[tex]\[
4 m + 3 = 0
\][/tex]
Subtract 3 from both sides:
[tex]\[
4 m = -3
\][/tex]
Now, divide both sides by 4:
[tex]\[
m = -\frac{3}{4}
\][/tex]
So, the solutions to the equation \((2 m + 3)(4 m + 3) = 0\) are:
[tex]\[
m = -\frac{3}{2} \quad \text{and} \quad m = -\frac{3}{4}
\][/tex]
Therefore, the solutions are:
[tex]\[
m = -\frac{3}{2} \quad \text{and} \quad m = -\frac{3}{4}
\][/tex]
