3x2-24x-48 is not factorable.
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(3x-12)(x-4)
16? using 16, you have (3x2 + 4)(3x2 + 4) = 9x2 + 24x + 16
x=-.25.
The idea is to solve the equation -3x2 + 24x - 19 = 0. You can use the quadratic formula for this, using a = -3, b = 24, c = 19. Or complete the square since dividing by -3 will give us 8x, an even coefficient. -3x2 + 24x - 19 = 0 (add and subtract 48 to the left side) -3x2 + 24x -48 + 29 = 0 (subtract 29 to both sides, and factor out -3) -3(x2 - 8x + 16) = -29 (divide by -3 to both sides) (x - 4)2 = 29/3 x - 4 = ± √(29/3) (add 4 to both sides) x = 4 ± √(29/3) (multiply by 3/3 inside the radical, if you want to rationalize the denominator) x = 4 ± (√87)/3
3x2 + 48 + 192 = 3x2 + 240 = 3 (x2+ 80)