(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 = -4u
(-12 + -4u + u2) = 0

Solving
-12 + -4u + 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}