Does an equation always have a solution

No, there is not always a solution to every equation. Infinitely many solutions is when both sides have the same equation. Ex: 4x - 1 = 4x - 1  No matter what you plug in.. it will be equal on both sides. 

No solution is something like this: 4x=4x+1If you subtract the 4x, you get 0 = -1
That is obviously not equal to -1, so there is no solution.
No matter what number you plug in for x, it will NOT be equal on both sides. 

To put it shortly:
Infinitely many solutions- EVERYTHING works
No solution- NOTHING works

y - y1 = m(x- x1)

y - (-5) = 2/3(x -0)

y + 5 = 2/3x

y = 2/3x - 5

10a^3+277a^2-132a-792

step-by-step explanation:

(2a+11)(5a-12)(foil)

=10a^2-24a+55a-132 =10a^2+31a-132

(10a^2+31a-132)(a+6)

=10a^3+60a^2+31a^2+186a^2-132a-792 =10a^3+277a^2-132a-792

i hope this is what you are looking for : )