(u-1)(u-9)=0

Solution for (u-1)(u-9)=0 equation:

Simplifying
(u + -1)(u + -9) = 0

Reorder the terms:
(-1 + u)(u + -9) = 0

Reorder the terms:
(-1 + u)(-9 + u) = 0

Multiply (-1 + u) * (-9 + u)
(-1(-9 + u) + u(-9 + u)) = 0
((-9 * -1 + u * -1) + u(-9 + u)) = 0
((9 + -1u) + u(-9 + u)) = 0
(9 + -1u + (-9 * u + u * u)) = 0
(9 + -1u + (-9u + u2)) = 0

Combine like terms: -1u + -9u = -10u
(9 + -10u + u2) = 0

Solving
9 + -10u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(1 + -1u)(9 + -1u) = 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 '(9 + -1u)' equal to zero and attempt to solve:

Simplifying
9 + -1u = 0

Solving
9 + -1u = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1u = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1u = 0 + -9
-1u = 0 + -9

Combine like terms: 0 + -9 = -9
-1u = -9

Divide each side by '-1'.
u = 9

Simplifying
u = 9
Solution
u = {1, 9}