(u-2)(4u-8)=5(u-2)u

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Solution for (u-2)(4u-8)=5(u-2)u equation: 


Simplifying
(u + -2)(4u + -8) = 5(u + -2) * u

Reorder the terms:
(-2 + u)(4u + -8) = 5(u + -2) * u

Reorder the terms:
(-2 + u)(-8 + 4u) = 5(u + -2) * u

Multiply (-2 + u) * (-8 + 4u)
(-2(-8 + 4u) + u(-8 + 4u)) = 5(u + -2) * u
((-8 * -2 + 4u * -2) + u(-8 + 4u)) = 5(u + -2) * u
((16 + -8u) + u(-8 + 4u)) = 5(u + -2) * u
(16 + -8u + (-8 * u + 4u * u)) = 5(u + -2) * u
(16 + -8u + (-8u + 4u2)) = 5(u + -2) * u

Combine like terms: -8u + -8u = -16u
(16 + -16u + 4u2) = 5(u + -2) * u

Reorder the terms:
16 + -16u + 4u2 = 5(-2 + u) * u

Reorder the terms for easier multiplication:
16 + -16u + 4u2 = 5u(-2 + u)
16 + -16u + 4u2 = (-2 * 5u + u * 5u)
16 + -16u + 4u2 = (-10u + 5u2)

Solving
16 + -16u + 4u2 = -10u + 5u2

Solving for variable 'u'.

Reorder the terms:
16 + -16u + 10u + 4u2 + -5u2 = -10u + 5u2 + 10u + -5u2

Combine like terms: -16u + 10u = -6u
16 + -6u + 4u2 + -5u2 = -10u + 5u2 + 10u + -5u2

Combine like terms: 4u2 + -5u2 = -1u2
16 + -6u + -1u2 = -10u + 5u2 + 10u + -5u2

Reorder the terms:
16 + -6u + -1u2 = -10u + 10u + 5u2 + -5u2

Combine like terms: -10u + 10u = 0
16 + -6u + -1u2 = 0 + 5u2 + -5u2
16 + -6u + -1u2 = 5u2 + -5u2

Combine like terms: 5u2 + -5u2 = 0
16 + -6u + -1u2 = 0

Factor a trinomial.
(2 + -1u)(8 + u) = 0


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 '(8 + u)' equal to zero and attempt to solve:

Simplifying
8 + u = 0

Solving
8 + u = 0

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

Add '-8' to each side of the equation.
8 + -8 + u = 0 + -8

Combine like terms: 8 + -8 = 0
0 + u = 0 + -8
u = 0 + -8

Combine like terms: 0 + -8 = -8
u = -8

Simplifying
u = -8
Solution
u = {2, -8}

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