2u^2+9u+13=(u+1)(u+1)

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Solution for 2u^2+9u+13=(u+1)(u+1) equation: 


Simplifying
2u2 + 9u + 13 = (u + 1)(u + 1)

Reorder the terms:
13 + 9u + 2u2 = (u + 1)(u + 1)

Reorder the terms:
13 + 9u + 2u2 = (1 + u)(u + 1)

Reorder the terms:
13 + 9u + 2u2 = (1 + u)(1 + u)

Multiply (1 + u) * (1 + u)
13 + 9u + 2u2 = (1(1 + u) + u(1 + u))
13 + 9u + 2u2 = ((1 * 1 + u * 1) + u(1 + u))
13 + 9u + 2u2 = ((1 + 1u) + u(1 + u))
13 + 9u + 2u2 = (1 + 1u + (1 * u + u * u))
13 + 9u + 2u2 = (1 + 1u + (1u + u2))

Combine like terms: 1u + 1u = 2u
13 + 9u + 2u2 = (1 + 2u + u2)

Solving
13 + 9u + 2u2 = 1 + 2u + u2

Solving for variable 'u'.

Reorder the terms:
13 + -1 + 9u + -2u + 2u2 + -1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Combine like terms: 13 + -1 = 12
12 + 9u + -2u + 2u2 + -1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Combine like terms: 9u + -2u = 7u
12 + 7u + 2u2 + -1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
12 + 7u + 1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Reorder the terms:
12 + 7u + 1u2 = 1 + -1 + 2u + -2u + u2 + -1u2

Combine like terms: 1 + -1 = 0
12 + 7u + 1u2 = 0 + 2u + -2u + u2 + -1u2
12 + 7u + 1u2 = 2u + -2u + u2 + -1u2

Combine like terms: 2u + -2u = 0
12 + 7u + 1u2 = 0 + u2 + -1u2
12 + 7u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
12 + 7u + 1u2 = 0

Factor a trinomial.
(4 + u)(3 + u) = 0


Subproblem 1
Set the factor '(4 + u)' equal to zero and attempt to solve:

Simplifying
4 + u = 0

Solving
4 + u = 0

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

Add '-4' to each side of the equation.
4 + -4 + u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + u = 0 + -4
u = 0 + -4

Combine like terms: 0 + -4 = -4
u = -4

Simplifying
u = -4

Subproblem 2
Set the factor '(3 + u)' equal to zero and attempt to solve:

Simplifying
3 + u = 0

Solving
3 + u = 0

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

Add '-3' to each side of the equation.
3 + -3 + u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + u = 0 + -3
u = 0 + -3

Combine like terms: 0 + -3 = -3
u = -3

Simplifying
u = -3
Solution
u = {-4, -3}

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