-4u(u-5)(u-4)=0

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Solution for -4u(u-5)(u-4)=0 equation: 


Simplifying
-4u(u + -5)(u + -4) = 0

Reorder the terms:
-4u(-5 + u)(u + -4) = 0

Reorder the terms:
-4u(-5 + u)(-4 + u) = 0

Multiply (-5 + u) * (-4 + u)
-4u(-5(-4 + u) + u(-4 + u)) = 0
-4u((-4 * -5 + u * -5) + u(-4 + u)) = 0
-4u((20 + -5u) + u(-4 + u)) = 0
-4u(20 + -5u + (-4 * u + u * u)) = 0
-4u(20 + -5u + (-4u + u2)) = 0

Combine like terms: -5u + -4u = -9u
-4u(20 + -9u + u2) = 0
(20 * -4u + -9u * -4u + u2 * -4u) = 0
(-80u + 36u2 + -4u3) = 0

Solving
-80u + 36u2 + -4u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '4u'.
4u(-20 + 9u + -1u2) = 0

Factor a trinomial.
4u((-5 + u)(4 + -1u)) = 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 '(-5 + u)' equal to zero and attempt to solve:

Simplifying
-5 + u = 0

Solving
-5 + u = 0

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

Add '5' to each side of the equation.
-5 + 5 + u = 0 + 5

Combine like terms: -5 + 5 = 0
0 + u = 0 + 5
u = 0 + 5

Combine like terms: 0 + 5 = 5
u = 5

Simplifying
u = 5

Subproblem 3
Set the factor '(4 + -1u)' equal to zero and attempt to solve:

Simplifying
4 + -1u = 0

Solving
4 + -1u = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1u = 0 + -4
-1u = 0 + -4

Combine like terms: 0 + -4 = -4
-1u = -4

Divide each side by '-1'.
u = 4

Simplifying
u = 4
Solution
u = {0, 5, 4}

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