2u^2+10u+13=(u+1)(u+1)

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Solution for 2u^2+10u+13=(u+1)(u+1) equation: 


Simplifying
2u2 + 10u + 13 = (u + 1)(u + 1)

Reorder the terms:
13 + 10u + 2u2 = (u + 1)(u + 1)

Reorder the terms:
13 + 10u + 2u2 = (1 + u)(u + 1)

Reorder the terms:
13 + 10u + 2u2 = (1 + u)(1 + u)

Multiply (1 + u) * (1 + u)
13 + 10u + 2u2 = (1(1 + u) + u(1 + u))
13 + 10u + 2u2 = ((1 * 1 + u * 1) + u(1 + u))
13 + 10u + 2u2 = ((1 + 1u) + u(1 + u))
13 + 10u + 2u2 = (1 + 1u + (1 * u + u * u))
13 + 10u + 2u2 = (1 + 1u + (1u + u2))

Combine like terms: 1u + 1u = 2u
13 + 10u + 2u2 = (1 + 2u + u2)

Solving
13 + 10u + 2u2 = 1 + 2u + u2

Solving for variable 'u'.

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

Combine like terms: 13 + -1 = 12
12 + 10u + -2u + 2u2 + -1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Combine like terms: 10u + -2u = 8u
12 + 8u + 2u2 + -1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
12 + 8u + 1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Reorder the terms:
12 + 8u + 1u2 = 1 + -1 + 2u + -2u + u2 + -1u2

Combine like terms: 1 + -1 = 0
12 + 8u + 1u2 = 0 + 2u + -2u + u2 + -1u2
12 + 8u + 1u2 = 2u + -2u + u2 + -1u2

Combine like terms: 2u + -2u = 0
12 + 8u + 1u2 = 0 + u2 + -1u2
12 + 8u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
12 + 8u + 1u2 = 0

Factor a trinomial.
(6 + u)(2 + 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 '(2 + u)' equal to zero and attempt to solve:

Simplifying
2 + u = 0

Solving
2 + u = 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 + u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + u = 0 + -2
u = 0 + -2

Combine like terms: 0 + -2 = -2
u = -2

Simplifying
u = -2
Solution
u = {-6, -2}

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