The equation that shows the factor for the quadratic equation is [tex](12x +3)(2x - 5) = 0[/tex]
The equation is given as:
[tex]24x^2 - 15 = 54x[/tex]
Equate to 0
[tex]24x^2 - 15 - 54x = 0[/tex]
Rewrite as:
[tex]24x^2 - 54x - 15 = 0[/tex]
Expand the above equation
[tex]24x^2 -60x + 6x - 15 = 0[/tex]
Factorize the above equation
[tex]12x(2x -5) + 3(2x - 5) = 0[/tex]
Factor out 2x - 5
[tex](12x +3)(2x - 5) = 0[/tex]
Hence, the equation that shows the factor for the quadratic equation is [tex](12x +3)(2x - 5) = 0[/tex]
Read more about quadratic factors at:
https://brainly.com/question/19573654
