2u^2+21u+40=0

Solution for 2u^2+21u+40=0 equation:

Simplifying
2u2 + 21u + 40 = 0

Reorder the terms:
40 + 21u + 2u2 = 0

Solving
40 + 21u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(8 + u)(5 + 2u) = 0

Subproblem 1
Set the factor '(8 + u)' equal to zero and attempt to solve:

Simplifying
8 + u = 0

Solving
8 + u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + u = 0 + -8

Combine like terms: 8 + -8 = 0
0 + u = 0 + -8
u = 0 + -8

Combine like terms: 0 + -8 = -8
u = -8

Simplifying
u = -8
Subproblem 2
Set the factor '(5 + 2u)' equal to zero and attempt to solve:

Simplifying
5 + 2u = 0

Solving
5 + 2u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + 2u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2u = 0 + -5
2u = 0 + -5

Combine like terms: 0 + -5 = -5
2u = -5

Divide each side by '2'.
u = -2.5

Simplifying
u = -2.5
Solution
u = {-8, -2.5}