With the information provided we can write:
6x^2 + 19x + c = (2x + 5)(ax + b)
Cross multiplying the terms on the right of the equation gives:
6x^2 + 19x + c = 2ax^2 + 5ax + 2bx + 5b
6x^2 + 19x + c = 2ax^2 + (5a + 2b)x + 5b
Therefore we know:
6x^2 = 2ax^2 Solving for a gives.
(6x^2)/x^2 = (2ax^2)/x^2
6 = 2a
(2a)/2 = 6/2
a = 3
Substituting this back into the equation gives:
6x^2 + 19x + c = 2*3x^2 + (5*3 + 2b)x + 5b
6x^2 + 19x + c = 6x^2 + (15 + 2b)x + 5b
Therefore we know:
19x = (15 + 2b)x Solving for b gives:
(19x)/x = ((15 + 2b)x)/x
19 = 15 + 2b
19 - 15 = 15 - 15 + 2b
4 = 2b
(2b)/2 = 4/2
b = 2
Substituting this back into the equation gives:
6x^2 + 19x + c = 6x^2 + (15 + 2*2)x + 5*2
6x^2 + 19x + c = 6x^2 + (15 + 4)x + 10
6x^2 + 19x + c = 6x^2 + 19x + 10
Therefore c = 10