1.solve the equation 2x^2+10x=0 . check your solution(s) and state the final solution set.
show all your work.

2x^2  + 10x = 0

we can take out x from both terms and we get:
x(2x + 10) = 0

now either x has to be equal to 0 or 2x + 10 has to be equal to zero in order for equation to be equal to 0. 

one solution is x=0 as stated above

other is:
2x + 10 = 0
2x = -10
x = -10/2 = -5

Answers are x=0 and x = -5.