2u^2+19u+46=u^2+8u+16

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Solution for 2u^2+19u+46=u^2+8u+16 equation: 


Simplifying
2u2 + 19u + 46 = u2 + 8u + 16

Reorder the terms:
46 + 19u + 2u2 = u2 + 8u + 16

Reorder the terms:
46 + 19u + 2u2 = 16 + 8u + u2

Solving
46 + 19u + 2u2 = 16 + 8u + u2

Solving for variable 'u'.

Reorder the terms:
46 + -16 + 19u + -8u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

Combine like terms: 46 + -16 = 30
30 + 19u + -8u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

Combine like terms: 19u + -8u = 11u
30 + 11u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
30 + 11u + 1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

Reorder the terms:
30 + 11u + 1u2 = 16 + -16 + 8u + -8u + u2 + -1u2

Combine like terms: 16 + -16 = 0
30 + 11u + 1u2 = 0 + 8u + -8u + u2 + -1u2
30 + 11u + 1u2 = 8u + -8u + u2 + -1u2

Combine like terms: 8u + -8u = 0
30 + 11u + 1u2 = 0 + u2 + -1u2
30 + 11u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
30 + 11u + 1u2 = 0

Factor a trinomial.
(6 + u)(5 + u) = 0


Subproblem 1
Set the factor '(6 + u)' equal to zero and attempt to solve:

Simplifying
6 + u = 0

Solving
6 + u = 0

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

Add '-6' to each side of the equation.
6 + -6 + u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + u = 0 + -6
u = 0 + -6

Combine like terms: 0 + -6 = -6
u = -6

Simplifying
u = -6

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 = {-6, -5}

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