10u^2-u-2=0

Solution for 10u^2-u-2=0 equation:

Simplifying
10u2 + -1u + -2 = 0

Reorder the terms:
-2 + -1u + 10u2 = 0

Solving
-2 + -1u + 10u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-2 + -5u)(1 + -2u) = 0

Subproblem 1
Set the factor '(-2 + -5u)' equal to zero and attempt to solve:

Simplifying
-2 + -5u = 0

Solving
-2 + -5u = 0

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

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

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

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

Divide each side by '-5'.
u = -0.4

Simplifying
u = -0.4
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 = {-0.4, 0.5}