-4u(u+2)(u-6)=0

Solution for -4u(u+2)(u-6)=0 equation:

Simplifying
-4u(u + 2)(u + -6) = 0

Reorder the terms:
-4u(2 + u)(u + -6) = 0

Reorder the terms:
-4u(2 + u)(-6 + u) = 0

Multiply (2 + u) * (-6 + u)
-4u(2(-6 + u) + u(-6 + u)) = 0
-4u((-6 * 2 + u * 2) + u(-6 + u)) = 0
-4u((-12 + 2u) + u(-6 + u)) = 0
-4u(-12 + 2u + (-6 * u + u * u)) = 0
-4u(-12 + 2u + (-6u + u2)) = 0

Combine like terms: 2u + -6u = -4u
-4u(-12 + -4u + u2) = 0
(-12 * -4u + -4u * -4u + u2 * -4u) = 0
(48u + 16u2 + -4u3) = 0

Solving
48u + 16u2 + -4u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '4u'.
4u(12 + 4u + -1u2) = 0

Factor a trinomial.
4u((6 + -1u)(2 + u)) = 0

Ignore the factor 4.
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 + -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 3
Set the factor '(2 + u)' equal to zero and attempt to solve:

Simplifying
2 + u = 0

Solving
2 + u = 0

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

Add '-2' to each side of the equation.
2 + -2 + u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + u = 0 + -2
u = 0 + -2

Combine like terms: 0 + -2 = -2
u = -2

Simplifying
u = -2
Solution
u = {0, 6, -2}