u^2-2u+20=(2u-4)(u+3)

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Solution for u^2-2u+20=(2u-4)(u+3) equation: 


Simplifying
u2 + -2u + 20 = (2u + -4)(u + 3)

Reorder the terms:
20 + -2u + u2 = (2u + -4)(u + 3)

Reorder the terms:
20 + -2u + u2 = (-4 + 2u)(u + 3)

Reorder the terms:
20 + -2u + u2 = (-4 + 2u)(3 + u)

Multiply (-4 + 2u) * (3 + u)
20 + -2u + u2 = (-4(3 + u) + 2u * (3 + u))
20 + -2u + u2 = ((3 * -4 + u * -4) + 2u * (3 + u))
20 + -2u + u2 = ((-12 + -4u) + 2u * (3 + u))
20 + -2u + u2 = (-12 + -4u + (3 * 2u + u * 2u))
20 + -2u + u2 = (-12 + -4u + (6u + 2u2))

Combine like terms: -4u + 6u = 2u
20 + -2u + u2 = (-12 + 2u + 2u2)

Solving
20 + -2u + u2 = -12 + 2u + 2u2

Solving for variable 'u'.

Reorder the terms:
20 + 12 + -2u + -2u + u2 + -2u2 = -12 + 2u + 2u2 + 12 + -2u + -2u2

Combine like terms: 20 + 12 = 32
32 + -2u + -2u + u2 + -2u2 = -12 + 2u + 2u2 + 12 + -2u + -2u2

Combine like terms: -2u + -2u = -4u
32 + -4u + u2 + -2u2 = -12 + 2u + 2u2 + 12 + -2u + -2u2

Combine like terms: u2 + -2u2 = -1u2
32 + -4u + -1u2 = -12 + 2u + 2u2 + 12 + -2u + -2u2

Reorder the terms:
32 + -4u + -1u2 = -12 + 12 + 2u + -2u + 2u2 + -2u2

Combine like terms: -12 + 12 = 0
32 + -4u + -1u2 = 0 + 2u + -2u + 2u2 + -2u2
32 + -4u + -1u2 = 2u + -2u + 2u2 + -2u2

Combine like terms: 2u + -2u = 0
32 + -4u + -1u2 = 0 + 2u2 + -2u2
32 + -4u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
32 + -4u + -1u2 = 0

Factor a trinomial.
(4 + -1u)(8 + u) = 0


Subproblem 1
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

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 = {4, -8}

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