u(u-6)(u-3)=

Solution for u(u-6)(u-3)= equation:

Simplifying
u(u + -6)(u + -3) = 0

Reorder the terms:
u(-6 + u)(u + -3) = 0

Reorder the terms:
u(-6 + u)(-3 + u) = 0

Multiply (-6 + u) * (-3 + u)
u(-6(-3 + u) + u(-3 + u)) = 0
u((-3 * -6 + u * -6) + u(-3 + u)) = 0
u((18 + -6u) + u(-3 + u)) = 0
u(18 + -6u + (-3 * u + u * u)) = 0
u(18 + -6u + (-3u + u2)) = 0

Combine like terms: -6u + -3u = -9u
u(18 + -9u + u2) = 0
(18 * u + -9u * u + u2 * u) = 0
(18u + -9u2 + u3) = 0

Solving
18u + -9u2 + u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), 'u'.
u(18 + -9u + u2) = 0

Factor a trinomial.
u((3 + -1u)(6 + -1u)) = 0

Subproblem 1
Set the factor 'u' equal to zero and attempt to solve:

Simplifying
u = 0

Solving
u = 0

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

Simplifying
u = 0
Subproblem 2
Set the factor '(3 + -1u)' equal to zero and attempt to solve:

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1u = 0 + -3
-1u = 0 + -3

Combine like terms: 0 + -3 = -3
-1u = -3

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Subproblem 3
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 = {0, 3, 6}