-5(u-2)(-u+4)=0

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Solution for -5(u-2)(-u+4)=0 equation: 


Simplifying
-5(u + -2)(-1u + 4) = 0

Reorder the terms:
-5(-2 + u)(-1u + 4) = 0

Reorder the terms:
-5(-2 + u)(4 + -1u) = 0

Multiply (-2 + u) * (4 + -1u)
-5(-2(4 + -1u) + u(4 + -1u)) = 0
-5((4 * -2 + -1u * -2) + u(4 + -1u)) = 0
-5((-8 + 2u) + u(4 + -1u)) = 0
-5(-8 + 2u + (4 * u + -1u * u)) = 0
-5(-8 + 2u + (4u + -1u2)) = 0

Combine like terms: 2u + 4u = 6u
-5(-8 + 6u + -1u2) = 0
(-8 * -5 + 6u * -5 + -1u2 * -5) = 0
(40 + -30u + 5u2) = 0

Solving
40 + -30u + 5u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '5'.
5(8 + -6u + u2) = 0

Factor a trinomial.
5((2 + -1u)(4 + -1u)) = 0

Ignore the factor 5.

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

Simplifying
2 + -1u = 0

Solving
2 + -1u = 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 + -1u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1u = 0 + -2
-1u = 0 + -2

Combine like terms: 0 + -2 = -2
-1u = -2

Divide each side by '-1'.
u = 2

Simplifying
u = 2

Subproblem 2
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 = {2, 4}

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