Solve by factorization 4x ^ 2 – 5x – 12 = 0

To solve the quadratic equation 4x^2 – 5x – 12 = 0 by factorization, we need to find two binomial factors that, when multiplied, give us the quadratic equation.

The equation can be factored as follows:

4x^2 – 5x – 12 = 0

(4x + 3)(x – 4) = 0

Setting each factor equal to zero, we can solve for x:

4x + 3 = 0 or x – 4 = 0

For 4x + 3 = 0:

4x = -3

x = -3/4

For x – 4 = 0:

x = 4

So, the solutions to the equation 4x^2 – 5x – 12 = 0 are:

x = -3/4 or x = 4.