u(u-18)-6(u-18)=0

Solution for u(u-18)-6(u-18)=0 equation:

Simplifying
u(u + -18) + -6(u + -18) = 0

Reorder the terms:
u(-18 + u) + -6(u + -18) = 0
(-18 * u + u * u) + -6(u + -18) = 0
(-18u + u2) + -6(u + -18) = 0

Reorder the terms:
-18u + u2 + -6(-18 + u) = 0
-18u + u2 + (-18 * -6 + u * -6) = 0
-18u + u2 + (108 + -6u) = 0

Reorder the terms:
108 + -18u + -6u + u2 = 0

Combine like terms: -18u + -6u = -24u
108 + -24u + u2 = 0

Solving
108 + -24u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6 + -1u)(18 + -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 '(18 + -1u)' equal to zero and attempt to solve:

Simplifying
18 + -1u = 0

Solving
18 + -1u = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1u = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1u = 0 + -18
-1u = 0 + -18

Combine like terms: 0 + -18 = -18
-1u = -18

Divide each side by '-1'.
u = 18

Simplifying
u = 18
Solution
u = {6, 18}