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

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


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

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

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

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

Combine like terms: -4u + -5u = -9u
-5u(20 + -9u + u2) = 0
(20 * -5u + -9u * -5u + u2 * -5u) = 0
(-100u + 45u2 + -5u3) = 0

Solving
-100u + 45u2 + -5u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '5u'.
5u(-20 + 9u + -1u2) = 0

Factor a trinomial.
5u((-5 + u)(4 + -1u)) = 0

Ignore the factor 5.

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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