(u+6)(u+6)=2u^2+11u+6

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Solution for (u+6)(u+6)=2u^2+11u+6 equation: 


Simplifying
(u + 6)(u + 6) = 2u2 + 11u + 6

Reorder the terms:
(6 + u)(u + 6) = 2u2 + 11u + 6

Reorder the terms:
(6 + u)(6 + u) = 2u2 + 11u + 6

Multiply (6 + u) * (6 + u)
(6(6 + u) + u(6 + u)) = 2u2 + 11u + 6
((6 * 6 + u * 6) + u(6 + u)) = 2u2 + 11u + 6
((36 + 6u) + u(6 + u)) = 2u2 + 11u + 6
(36 + 6u + (6 * u + u * u)) = 2u2 + 11u + 6
(36 + 6u + (6u + u2)) = 2u2 + 11u + 6

Combine like terms: 6u + 6u = 12u
(36 + 12u + u2) = 2u2 + 11u + 6

Reorder the terms:
36 + 12u + u2 = 6 + 11u + 2u2

Solving
36 + 12u + u2 = 6 + 11u + 2u2

Solving for variable 'u'.

Reorder the terms:
36 + -6 + 12u + -11u + u2 + -2u2 = 6 + 11u + 2u2 + -6 + -11u + -2u2

Combine like terms: 36 + -6 = 30
30 + 12u + -11u + u2 + -2u2 = 6 + 11u + 2u2 + -6 + -11u + -2u2

Combine like terms: 12u + -11u = 1u
30 + 1u + u2 + -2u2 = 6 + 11u + 2u2 + -6 + -11u + -2u2

Combine like terms: u2 + -2u2 = -1u2
30 + 1u + -1u2 = 6 + 11u + 2u2 + -6 + -11u + -2u2

Reorder the terms:
30 + 1u + -1u2 = 6 + -6 + 11u + -11u + 2u2 + -2u2

Combine like terms: 6 + -6 = 0
30 + 1u + -1u2 = 0 + 11u + -11u + 2u2 + -2u2
30 + 1u + -1u2 = 11u + -11u + 2u2 + -2u2

Combine like terms: 11u + -11u = 0
30 + 1u + -1u2 = 0 + 2u2 + -2u2
30 + 1u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
30 + 1u + -1u2 = 0

Factor a trinomial.
(6 + -1u)(5 + u) = 0


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

Simplifying
6 + -1u = 0

Solving
6 + -1u = 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 + -1u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1u = 0 + -6
-1u = 0 + -6

Combine like terms: 0 + -6 = -6
-1u = -6

Divide each side by '-1'.
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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