(u-2)(u-6)=0

Solution for (u-2)(u-6)=0 equation:

Simplifying
(u + -2)(u + -6) = 0

Reorder the terms:
(-2 + u)(u + -6) = 0

Reorder the terms:
(-2 + u)(-6 + u) = 0

Multiply (-2 + u) * (-6 + u)
(-2(-6 + u) + u(-6 + u)) = 0
((-6 * -2 + u * -2) + u(-6 + u)) = 0
((12 + -2u) + u(-6 + u)) = 0
(12 + -2u + (-6 * u + u * u)) = 0
(12 + -2u + (-6u + u2)) = 0

Combine like terms: -2u + -6u = -8u
(12 + -8u + u2) = 0

Solving
12 + -8u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(2 + -1u)(6 + -1u) = 0

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

Simplifying
2 + -1u = 0

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

Combine like terms: 2 + -2 = 0
0 + -1u = 0 + -2
-1u = 0 + -2

Combine like terms: 0 + -2 = -2
-1u = -2

Divide each side by '-1'.
u = 2

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

Simplifying
6 + -1u = 0

Solving
6 + -1u = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1u = 0 + -6

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

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

Divide each side by '-1'.
u = 6

Simplifying
u = 6
Solution
u = {2, 6}