-5u+9=u^2+2u+1

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Solution for -5u+9=u^2+2u+1 equation: 


Simplifying
-5u + 9 = u2 + 2u + 1

Reorder the terms:
9 + -5u = u2 + 2u + 1

Reorder the terms:
9 + -5u = 1 + 2u + u2

Solving
9 + -5u = 1 + 2u + u2

Solving for variable 'u'.

Reorder the terms:
9 + -1 + -5u + -2u + -1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Combine like terms: 9 + -1 = 8
8 + -5u + -2u + -1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Combine like terms: -5u + -2u = -7u
8 + -7u + -1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Reorder the terms:
8 + -7u + -1u2 = 1 + -1 + 2u + -2u + u2 + -1u2

Combine like terms: 1 + -1 = 0
8 + -7u + -1u2 = 0 + 2u + -2u + u2 + -1u2
8 + -7u + -1u2 = 2u + -2u + u2 + -1u2

Combine like terms: 2u + -2u = 0
8 + -7u + -1u2 = 0 + u2 + -1u2
8 + -7u + -1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
8 + -7u + -1u2 = 0

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


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

Simplifying
1 + -1u = 0

Solving
1 + -1u = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1u = 0 + -1

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

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

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

Simplifying
u = 1

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 = {1, -8}

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