Answer:

To solve these quadratic equations by factoring, we'll first attempt to identify perfect square trinomials.

1. **9m² - 12m + 4 = 0**

This equation can be factored as:

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

Now, apply the zero-product property:

3m - 2 = 0

3m = 2

m = 2/3

2. **4x² - 28x = -49**

First, move all terms to one side to set the equation to zero:

4x² - 28x + 49 = 0

Now, this equation is a perfect square trinomial:

(2x - 7)(2x - 7) = 0

Apply the zero-product property:

2x - 7 = 0

2x = 7

x = 7/2

3. **4s² + 9 = 12s**

Rearrange the terms:

4s² - 12s + 9 = 0

This equation can be factored as a perfect square trinomial:

(2s - 3)(2s - 3) = 0

Apply the zero-product property:

2s - 3 = 0

2s = 3

s = 3/2

So, the solutions to the equations are:

1. m = 2/3

2. x = 7/2

3. s = 3/2

Step-by-step explanation:

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