Sure, let's solve the equation \((2m + 3)(4m + 3) = 0\) step by step.
### Step 1: Identify the factors
We are given the equation in factored form:
[tex]\[
(2m + 3)(4m + 3) = 0
\][/tex]
### Step 2: Set each factor equal to zero
For the product of two factors to be zero, at least one of the factors must be zero. Therefore, we can set each factor to zero and solve for \(m\).
#### Factor 1:
[tex]\[
2m + 3 = 0
\][/tex]
#### Factor 2:
[tex]\[
4m + 3 = 0
\][/tex]
### Step 3: Solve each equation
#### Solving \(2m + 3 = 0\):
[tex]\[
2m + 3 = 0
\][/tex]
Subtract 3 from both sides:
[tex]\[
2m = -3
\][/tex]
Divide by 2:
[tex]\[
m = -\frac{3}{2}
\][/tex]
#### Solving \(4m + 3 = 0\):
[tex]\[
4m + 3 = 0
\][/tex]
Subtract 3 from both sides:
[tex]\[
4m = -3
\][/tex]
Divide by 4:
[tex]\[
m = -\frac{3}{4}
\][/tex]
### Step 4: Write the final solutions
The solutions to the equation \((2m + 3)(4m + 3) = 0\) are:
[tex]\[
m = -\frac{3}{2} \quad \text{and} \quad m = -\frac{3}{4}
\][/tex]
