(u-1)(6u-1)=0

Solution for (u-1)(6u-1)=0 equation:

Simplifying
(u + -1)(6u + -1) = 0

Reorder the terms:
(-1 + u)(6u + -1) = 0

Reorder the terms:
(-1 + u)(-1 + 6u) = 0

Multiply (-1 + u) * (-1 + 6u)
(-1(-1 + 6u) + u(-1 + 6u)) = 0
((-1 * -1 + 6u * -1) + u(-1 + 6u)) = 0
((1 + -6u) + u(-1 + 6u)) = 0
(1 + -6u + (-1 * u + 6u * u)) = 0
(1 + -6u + (-1u + 6u2)) = 0

Combine like terms: -6u + -1u = -7u
(1 + -7u + 6u2) = 0

Solving
1 + -7u + 6u2 = 0

Solving for variable 'u'.

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

Subproblem 1
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
Subproblem 2
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
Solution
u = {0.1666666667, 1}