2v^2+12v+19=(v+2)(v+2)

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Solution for 2v^2+12v+19=(v+2)(v+2) equation: 


Simplifying
2v2 + 12v + 19 = (v + 2)(v + 2)

Reorder the terms:
19 + 12v + 2v2 = (v + 2)(v + 2)

Reorder the terms:
19 + 12v + 2v2 = (2 + v)(v + 2)

Reorder the terms:
19 + 12v + 2v2 = (2 + v)(2 + v)

Multiply (2 + v) * (2 + v)
19 + 12v + 2v2 = (2(2 + v) + v(2 + v))
19 + 12v + 2v2 = ((2 * 2 + v * 2) + v(2 + v))
19 + 12v + 2v2 = ((4 + 2v) + v(2 + v))
19 + 12v + 2v2 = (4 + 2v + (2 * v + v * v))
19 + 12v + 2v2 = (4 + 2v + (2v + v2))

Combine like terms: 2v + 2v = 4v
19 + 12v + 2v2 = (4 + 4v + v2)

Solving
19 + 12v + 2v2 = 4 + 4v + v2

Solving for variable 'v'.

Reorder the terms:
19 + -4 + 12v + -4v + 2v2 + -1v2 = 4 + 4v + v2 + -4 + -4v + -1v2

Combine like terms: 19 + -4 = 15
15 + 12v + -4v + 2v2 + -1v2 = 4 + 4v + v2 + -4 + -4v + -1v2

Combine like terms: 12v + -4v = 8v
15 + 8v + 2v2 + -1v2 = 4 + 4v + v2 + -4 + -4v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
15 + 8v + 1v2 = 4 + 4v + v2 + -4 + -4v + -1v2

Reorder the terms:
15 + 8v + 1v2 = 4 + -4 + 4v + -4v + v2 + -1v2

Combine like terms: 4 + -4 = 0
15 + 8v + 1v2 = 0 + 4v + -4v + v2 + -1v2
15 + 8v + 1v2 = 4v + -4v + v2 + -1v2

Combine like terms: 4v + -4v = 0
15 + 8v + 1v2 = 0 + v2 + -1v2
15 + 8v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
15 + 8v + 1v2 = 0

Factor a trinomial.
(5 + v)(3 + v) = 0


Subproblem 1
Set the factor '(5 + v)' equal to zero and attempt to solve:

Simplifying
5 + v = 0

Solving
5 + v = 0

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

Add '-5' to each side of the equation.
5 + -5 + v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + v = 0 + -5
v = 0 + -5

Combine like terms: 0 + -5 = -5
v = -5

Simplifying
v = -5

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

Simplifying
3 + v = 0

Solving
3 + v = 0

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

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

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

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

Simplifying
v = -3
Solution
v = {-5, -3}

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