u^2+10u+21=2u^2+13u+11

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Solution for u^2+10u+21=2u^2+13u+11 equation: 


Simplifying
u2 + 10u + 21 = 2u2 + 13u + 11

Reorder the terms:
21 + 10u + u2 = 2u2 + 13u + 11

Reorder the terms:
21 + 10u + u2 = 11 + 13u + 2u2

Solving
21 + 10u + u2 = 11 + 13u + 2u2

Solving for variable 'u'.

Reorder the terms:
21 + -11 + 10u + -13u + u2 + -2u2 = 11 + 13u + 2u2 + -11 + -13u + -2u2

Combine like terms: 21 + -11 = 10
10 + 10u + -13u + u2 + -2u2 = 11 + 13u + 2u2 + -11 + -13u + -2u2

Combine like terms: 10u + -13u = -3u
10 + -3u + u2 + -2u2 = 11 + 13u + 2u2 + -11 + -13u + -2u2

Combine like terms: u2 + -2u2 = -1u2
10 + -3u + -1u2 = 11 + 13u + 2u2 + -11 + -13u + -2u2

Reorder the terms:
10 + -3u + -1u2 = 11 + -11 + 13u + -13u + 2u2 + -2u2

Combine like terms: 11 + -11 = 0
10 + -3u + -1u2 = 0 + 13u + -13u + 2u2 + -2u2
10 + -3u + -1u2 = 13u + -13u + 2u2 + -2u2

Combine like terms: 13u + -13u = 0
10 + -3u + -1u2 = 0 + 2u2 + -2u2
10 + -3u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
10 + -3u + -1u2 = 0

Factor a trinomial.
(2 + -1u)(5 + 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 '(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
Solution
u = {2, -5}

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