21u^2-8u-5=0

Solution for 21u^2-8u-5=0 equation:

Simplifying
21u2 + -8u + -5 = 0

Reorder the terms:
-5 + -8u + 21u2 = 0

Solving
-5 + -8u + 21u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1 + -3u)(5 + -7u) = 0

Subproblem 1
Set the factor '(-1 + -3u)' equal to zero and attempt to solve:

Simplifying
-1 + -3u = 0

Solving
-1 + -3u = 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 + -3u = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3u = 0 + 1
-3u = 0 + 1

Combine like terms: 0 + 1 = 1
-3u = 1

Divide each side by '-3'.
u = -0.3333333333

Simplifying
u = -0.3333333333
Subproblem 2
Set the factor '(5 + -7u)' equal to zero and attempt to solve:

Simplifying
5 + -7u = 0

Solving
5 + -7u = 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 + -7u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7u = 0 + -5
-7u = 0 + -5

Combine like terms: 0 + -5 = -5
-7u = -5

Divide each side by '-7'.
u = 0.7142857143

Simplifying
u = 0.7142857143
Solution
u = {-0.3333333333, 0.7142857143}