(u-6)(u-4)=0

Solution for (u-6)(u-4)=0 equation:

Simplifying
(u + -6)(u + -4) = 0

Reorder the terms:
(-6 + u)(u + -4) = 0

Reorder the terms:
(-6 + u)(-4 + u) = 0

Multiply (-6 + u) * (-4 + u)
(-6(-4 + u) + u(-4 + u)) = 0
((-4 * -6 + u * -6) + u(-4 + u)) = 0
((24 + -6u) + u(-4 + u)) = 0
(24 + -6u + (-4 * u + u * u)) = 0
(24 + -6u + (-4u + u2)) = 0

Combine like terms: -6u + -4u = -10u
(24 + -10u + u2) = 0

Solving
24 + -10u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(4 + -1u)(6 + -1u) = 0

Subproblem 1
Set the factor '(4 + -1u)' equal to zero and attempt to solve:

Simplifying
4 + -1u = 0

Solving
4 + -1u = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1u = 0 + -4
-1u = 0 + -4

Combine like terms: 0 + -4 = -4
-1u = -4

Divide each side by '-1'.
u = 4

Simplifying
u = 4
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 = {4, 6}