2u^2-3u-19=u^2-2u+1

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Solution for 2u^2-3u-19=u^2-2u+1 equation: 


Simplifying
2u2 + -3u + -19 = u2 + -2u + 1

Reorder the terms:
-19 + -3u + 2u2 = u2 + -2u + 1

Reorder the terms:
-19 + -3u + 2u2 = 1 + -2u + u2

Solving
-19 + -3u + 2u2 = 1 + -2u + u2

Solving for variable 'u'.

Reorder the terms:
-19 + -1 + -3u + 2u + 2u2 + -1u2 = 1 + -2u + u2 + -1 + 2u + -1u2

Combine like terms: -19 + -1 = -20
-20 + -3u + 2u + 2u2 + -1u2 = 1 + -2u + u2 + -1 + 2u + -1u2

Combine like terms: -3u + 2u = -1u
-20 + -1u + 2u2 + -1u2 = 1 + -2u + u2 + -1 + 2u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
-20 + -1u + 1u2 = 1 + -2u + u2 + -1 + 2u + -1u2

Reorder the terms:
-20 + -1u + 1u2 = 1 + -1 + -2u + 2u + u2 + -1u2

Combine like terms: 1 + -1 = 0
-20 + -1u + 1u2 = 0 + -2u + 2u + u2 + -1u2
-20 + -1u + 1u2 = -2u + 2u + u2 + -1u2

Combine like terms: -2u + 2u = 0
-20 + -1u + 1u2 = 0 + u2 + -1u2
-20 + -1u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-20 + -1u + 1u2 = 0

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

Simplifying
5 + -1u = 0

Solving
5 + -1u = 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 + -1u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1u = 0 + -5
-1u = 0 + -5

Combine like terms: 0 + -5 = -5
-1u = -5

Divide each side by '-1'.
u = 5

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

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