2v^2+12v+16=(v+2)(v+2)

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Solution for 2v^2+12v+16=(v+2)(v+2) equation: 


Simplifying
2v2 + 12v + 16 = (v + 2)(v + 2)

Reorder the terms:
16 + 12v + 2v2 = (v + 2)(v + 2)

Reorder the terms:
16 + 12v + 2v2 = (2 + v)(v + 2)

Reorder the terms:
16 + 12v + 2v2 = (2 + v)(2 + v)

Multiply (2 + v) * (2 + v)
16 + 12v + 2v2 = (2(2 + v) + v(2 + v))
16 + 12v + 2v2 = ((2 * 2 + v * 2) + v(2 + v))
16 + 12v + 2v2 = ((4 + 2v) + v(2 + v))
16 + 12v + 2v2 = (4 + 2v + (2 * v + v * v))
16 + 12v + 2v2 = (4 + 2v + (2v + v2))

Combine like terms: 2v + 2v = 4v
16 + 12v + 2v2 = (4 + 4v + v2)

Solving
16 + 12v + 2v2 = 4 + 4v + v2

Solving for variable 'v'.

Reorder the terms:
16 + -4 + 12v + -4v + 2v2 + -1v2 = 4 + 4v + v2 + -4 + -4v + -1v2

Combine like terms: 16 + -4 = 12
12 + 12v + -4v + 2v2 + -1v2 = 4 + 4v + v2 + -4 + -4v + -1v2

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

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

Reorder the terms:
12 + 8v + 1v2 = 4 + -4 + 4v + -4v + v2 + -1v2

Combine like terms: 4 + -4 = 0
12 + 8v + 1v2 = 0 + 4v + -4v + v2 + -1v2
12 + 8v + 1v2 = 4v + -4v + v2 + -1v2

Combine like terms: 4v + -4v = 0
12 + 8v + 1v2 = 0 + v2 + -1v2
12 + 8v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
12 + 8v + 1v2 = 0

Factor a trinomial.
(6 + v)(2 + v) = 0


Subproblem 1
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 0

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

Add '-6' to each side of the equation.
6 + -6 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
v = -6

Simplifying
v = -6

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

Simplifying
2 + v = 0

Solving
2 + v = 0

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

Add '-2' to each side of the equation.
2 + -2 + v = 0 + -2

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

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

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

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