u(6u+5)=1

Solution for u(6u+5)=1 equation:

Simplifying
u(6u + 5) = 1

Reorder the terms:
u(5 + 6u) = 1
(5 * u + 6u * u) = 1
(5u + 6u2) = 1

Solving
5u + 6u2 = 1

Solving for variable 'u'.

Reorder the terms:
-1 + 5u + 6u2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 5u + 6u2 = 0

Factor a trinomial.
(-1 + -1u)(1 + -6u) = 0

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

Simplifying
-1 + -1u = 0

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

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

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

Divide each side by '-1'.
u = -1

Simplifying
u = -1
Subproblem 2
Set the factor '(1 + -6u)' equal to zero and attempt to solve:

Simplifying
1 + -6u = 0

Solving
1 + -6u = 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 + -6u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6u = 0 + -1
-6u = 0 + -1

Combine like terms: 0 + -1 = -1
-6u = -1

Divide each side by '-6'.
u = 0.1666666667

Simplifying
u = 0.1666666667
Solution
u = {-1, 0.1666666667}