u(u-10)-6(u-10)=0

Solution for u(u-10)-6(u-10)=0 equation:

Simplifying
u(u + -10) + -6(u + -10) = 0

Reorder the terms:
u(-10 + u) + -6(u + -10) = 0
(-10 * u + u * u) + -6(u + -10) = 0
(-10u + u2) + -6(u + -10) = 0

Reorder the terms:
-10u + u2 + -6(-10 + u) = 0
-10u + u2 + (-10 * -6 + u * -6) = 0
-10u + u2 + (60 + -6u) = 0

Reorder the terms:
60 + -10u + -6u + u2 = 0

Combine like terms: -10u + -6u = -16u
60 + -16u + u2 = 0

Solving
60 + -16u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6 + -1u)(10 + -1u) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(10 + -1u)' equal to zero and attempt to solve:

Simplifying
10 + -1u = 0

Solving
10 + -1u = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1u = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1u = 0 + -10
-1u = 0 + -10

Combine like terms: 0 + -10 = -10
-1u = -10

Divide each side by '-1'.
u = 10

Simplifying
u = 10
Solution
u = {6, 10}