2v^2-4v+9=(v+1)(v+1)

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Solution for 2v^2-4v+9=(v+1)(v+1) equation: 


Simplifying
2v2 + -4v + 9 = (v + 1)(v + 1)

Reorder the terms:
9 + -4v + 2v2 = (v + 1)(v + 1)

Reorder the terms:
9 + -4v + 2v2 = (1 + v)(v + 1)

Reorder the terms:
9 + -4v + 2v2 = (1 + v)(1 + v)

Multiply (1 + v) * (1 + v)
9 + -4v + 2v2 = (1(1 + v) + v(1 + v))
9 + -4v + 2v2 = ((1 * 1 + v * 1) + v(1 + v))
9 + -4v + 2v2 = ((1 + 1v) + v(1 + v))
9 + -4v + 2v2 = (1 + 1v + (1 * v + v * v))
9 + -4v + 2v2 = (1 + 1v + (1v + v2))

Combine like terms: 1v + 1v = 2v
9 + -4v + 2v2 = (1 + 2v + v2)

Solving
9 + -4v + 2v2 = 1 + 2v + v2

Solving for variable 'v'.

Reorder the terms:
9 + -1 + -4v + -2v + 2v2 + -1v2 = 1 + 2v + v2 + -1 + -2v + -1v2

Combine like terms: 9 + -1 = 8
8 + -4v + -2v + 2v2 + -1v2 = 1 + 2v + v2 + -1 + -2v + -1v2

Combine like terms: -4v + -2v = -6v
8 + -6v + 2v2 + -1v2 = 1 + 2v + v2 + -1 + -2v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
8 + -6v + 1v2 = 1 + 2v + v2 + -1 + -2v + -1v2

Reorder the terms:
8 + -6v + 1v2 = 1 + -1 + 2v + -2v + v2 + -1v2

Combine like terms: 1 + -1 = 0
8 + -6v + 1v2 = 0 + 2v + -2v + v2 + -1v2
8 + -6v + 1v2 = 2v + -2v + v2 + -1v2

Combine like terms: 2v + -2v = 0
8 + -6v + 1v2 = 0 + v2 + -1v2
8 + -6v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
8 + -6v + 1v2 = 0

Factor a trinomial.
(2 + -1v)(4 + -1v) = 0


Subproblem 1
Set the factor '(2 + -1v)' equal to zero and attempt to solve:

Simplifying
2 + -1v = 0

Solving
2 + -1v = 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 + -1v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1v = 0 + -2
-1v = 0 + -2

Combine like terms: 0 + -2 = -2
-1v = -2

Divide each side by '-1'.
v = 2

Simplifying
v = 2

Subproblem 2
Set the factor '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {2, 4}

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