-3u(u-1)(u-6)=0

Solution for -3u(u-1)(u-6)=0 equation:

Simplifying
-3u(u + -1)(u + -6) = 0

Reorder the terms:
-3u(-1 + u)(u + -6) = 0

Reorder the terms:
-3u(-1 + u)(-6 + u) = 0

Multiply (-1 + u) * (-6 + u)
-3u(-1(-6 + u) + u(-6 + u)) = 0
-3u((-6 * -1 + u * -1) + u(-6 + u)) = 0
-3u((6 + -1u) + u(-6 + u)) = 0
-3u(6 + -1u + (-6 * u + u * u)) = 0
-3u(6 + -1u + (-6u + u2)) = 0

Combine like terms: -1u + -6u = -7u
-3u(6 + -7u + u2) = 0
(6 * -3u + -7u * -3u + u2 * -3u) = 0
(-18u + 21u2 + -3u3) = 0

Solving
-18u + 21u2 + -3u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3u'.
3u(-6 + 7u + -1u2) = 0

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

Ignore the factor 3.
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 '(-6 + u)' equal to zero and attempt to solve:

Simplifying
-6 + u = 0

Solving
-6 + u = 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 + u = 0 + 6

Combine like terms: -6 + 6 = 0
0 + u = 0 + 6
u = 0 + 6

Combine like terms: 0 + 6 = 6
u = 6

Simplifying
u = 6
Subproblem 3
Set the factor '(1 + -1u)' equal to zero and attempt to solve:

Simplifying
1 + -1u = 0

Solving
1 + -1u = 0

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

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

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

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

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

Simplifying
u = 1
Solution
u = {0, 6, 1}