2u^2+4u+11=(u+4)(u+4)

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Solution for 2u^2+4u+11=(u+4)(u+4) equation: 


Simplifying
2u2 + 4u + 11 = (u + 4)(u + 4)

Reorder the terms:
11 + 4u + 2u2 = (u + 4)(u + 4)

Reorder the terms:
11 + 4u + 2u2 = (4 + u)(u + 4)

Reorder the terms:
11 + 4u + 2u2 = (4 + u)(4 + u)

Multiply (4 + u) * (4 + u)
11 + 4u + 2u2 = (4(4 + u) + u(4 + u))
11 + 4u + 2u2 = ((4 * 4 + u * 4) + u(4 + u))
11 + 4u + 2u2 = ((16 + 4u) + u(4 + u))
11 + 4u + 2u2 = (16 + 4u + (4 * u + u * u))
11 + 4u + 2u2 = (16 + 4u + (4u + u2))

Combine like terms: 4u + 4u = 8u
11 + 4u + 2u2 = (16 + 8u + u2)

Solving
11 + 4u + 2u2 = 16 + 8u + u2

Solving for variable 'u'.

Reorder the terms:
11 + -16 + 4u + -8u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

Combine like terms: 11 + -16 = -5
-5 + 4u + -8u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

Combine like terms: 4u + -8u = -4u
-5 + -4u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
-5 + -4u + 1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

Reorder the terms:
-5 + -4u + 1u2 = 16 + -16 + 8u + -8u + u2 + -1u2

Combine like terms: 16 + -16 = 0
-5 + -4u + 1u2 = 0 + 8u + -8u + u2 + -1u2
-5 + -4u + 1u2 = 8u + -8u + u2 + -1u2

Combine like terms: 8u + -8u = 0
-5 + -4u + 1u2 = 0 + u2 + -1u2
-5 + -4u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-5 + -4u + 1u2 = 0

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

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