2u^2+13u+20=(u+4)(u+4)

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Solution for 2u^2+13u+20=(u+4)(u+4) equation: 


Simplifying
2u2 + 13u + 20 = (u + 4)(u + 4)

Reorder the terms:
20 + 13u + 2u2 = (u + 4)(u + 4)

Reorder the terms:
20 + 13u + 2u2 = (4 + u)(u + 4)

Reorder the terms:
20 + 13u + 2u2 = (4 + u)(4 + u)

Multiply (4 + u) * (4 + u)
20 + 13u + 2u2 = (4(4 + u) + u(4 + u))
20 + 13u + 2u2 = ((4 * 4 + u * 4) + u(4 + u))
20 + 13u + 2u2 = ((16 + 4u) + u(4 + u))
20 + 13u + 2u2 = (16 + 4u + (4 * u + u * u))
20 + 13u + 2u2 = (16 + 4u + (4u + u2))

Combine like terms: 4u + 4u = 8u
20 + 13u + 2u2 = (16 + 8u + u2)

Solving
20 + 13u + 2u2 = 16 + 8u + u2

Solving for variable 'u'.

Reorder the terms:
20 + -16 + 13u + -8u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

Combine like terms: 20 + -16 = 4
4 + 13u + -8u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

Combine like terms: 13u + -8u = 5u
4 + 5u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

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

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

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

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

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

Factor a trinomial.
(4 + u)(1 + 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 '(1 + u)' equal to zero and attempt to solve:

Simplifying
1 + u = 0

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

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

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

Simplifying
u = -1
Solution
u = {-4, -1}

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