2u^2+21u+10=0

Solution for 2u^2+21u+10=0 equation:

Simplifying
2u2 + 21u + 10 = 0

Reorder the terms:
10 + 21u + 2u2 = 0

Solving
10 + 21u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(10 + u)(1 + 2u) = 0

Subproblem 1
Set the factor '(10 + u)' equal to zero and attempt to solve:

Simplifying
10 + u = 0

Solving
10 + u = 0

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

Add '-10' to each side of the equation.
10 + -10 + u = 0 + -10

Combine like terms: 10 + -10 = 0
0 + u = 0 + -10
u = 0 + -10

Combine like terms: 0 + -10 = -10
u = -10

Simplifying
u = -10
Subproblem 2
Set the factor '(1 + 2u)' equal to zero and attempt to solve:

Simplifying
1 + 2u = 0

Solving
1 + 2u = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2u = 0 + -1
2u = 0 + -1

Combine like terms: 0 + -1 = -1
2u = -1

Divide each side by '2'.
u = -0.5

Simplifying
u = -0.5
Solution
u = {-10, -0.5}