(x + 1)(2x + 3)(3x + 4) = (6x2 + 5)(x - 3)
Multiply (x + 1)(2x + 3) and (6x2 + 5)(x - 3)
(2x2 + 5x + 3 )(3x + 4) = 6x3 - 18x2 + 5x - 15
Multiply (2x2 + 5x + 3 )(3x + 4)
6x3 + 8x2 + 15x2 + 20x + 9x + 12 = 6x3 - 18x2 + 5x - 15
Combine like terms on the left side.
6x3 + 23x2 + 29x + 12 = 6x3 - 18x2 + 5x - 15
Subtract 6x3 from both sides of the equation.
23x2 + 29x + 12 = -18x2 + 5x - 15
Add 18x2 to both sides of the equation.
41x2 + 29x + 12 = 5x - 15
Subtract 5x from both sides.
41x2 + 24x + 12 = -15
Add 15 to both sides.
41x2 + 24x + 27 = 0
The GCF of 41, 24, and 27 is 1
0 = 41x2 + 24x + 27
Now it is in the form 0 = Ax2 + Bx + C where A, B, and C are positive integers with a GCF of 1.
A + B + C = 41 + 24 + 27 = 92