Solve by factoring.4 m squared minus 5 m minus 6equals0Question content area bottomPart 1mequalsenter your response here ​(Use a comma to separate answers as​ needed.)

Answer 1

To solve the equation \( 4m^2 - 5m - 6 = 0 \) by factoring, we need to find factors of the quadratic expression.

1. Start by identifying \( a \), \( b \), and \( c \) in the quadratic equation \( ax^2 + bx + c \):

   • \( a = 4 \)
   • \( b = -5 \)
   • \( c = -6 \)

2. To factor the quadratic, we look for two numbers that multiply to \( ac \) (which is \( 4 \times -6 = -24 \)) and add up to \( b \) (which is \(-5\)).

3. The two numbers that satisfy these conditions are \( -8 \) and \( 3 \):

   • \( -8 \times 3 = -24 \)
   • \( -8 + 3 = -5 \)

4. Rewrite the middle term using these two numbers: \[ 4m^2 - 8m + 3m - 6 = 0 \]

5. Factor by grouping: \[ (4m^2 - 8m) + (3m - 6) = 0 \] \[ 4m(m - 2) + 3(m - 2) = 0 \]

6. Now factor out the common factor \( (m - 2) \): \[ (m - 2)(4m + 3) = 0 \]

7. Set each factor equal to zero: \[ m - 2 = 0 \quad \text{or} \quad 4m + 3 = 0 \]

8. Solve for \( m \):

   • From \( m - 2 = 0 \): \[ m = 2 \]
   • From \( 4m + 3 = 0 \): \[ 4m = -3 \quad \Rightarrow \quad m = -\frac{3}{4} \]

Thus, the solutions are: \[ m = 2, -\frac{3}{4} \]

In comma-separated form, the final answer is: \[ \boxed{2, -\frac{3}{4}} \]