2v^2+6v+25=(v-2)(v-2)

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Solution for 2v^2+6v+25=(v-2)(v-2) equation: 


Simplifying
2v2 + 6v + 25 = (v + -2)(v + -2)

Reorder the terms:
25 + 6v + 2v2 = (v + -2)(v + -2)

Reorder the terms:
25 + 6v + 2v2 = (-2 + v)(v + -2)

Reorder the terms:
25 + 6v + 2v2 = (-2 + v)(-2 + v)

Multiply (-2 + v) * (-2 + v)
25 + 6v + 2v2 = (-2(-2 + v) + v(-2 + v))
25 + 6v + 2v2 = ((-2 * -2 + v * -2) + v(-2 + v))
25 + 6v + 2v2 = ((4 + -2v) + v(-2 + v))
25 + 6v + 2v2 = (4 + -2v + (-2 * v + v * v))
25 + 6v + 2v2 = (4 + -2v + (-2v + v2))

Combine like terms: -2v + -2v = -4v
25 + 6v + 2v2 = (4 + -4v + v2)

Solving
25 + 6v + 2v2 = 4 + -4v + v2

Solving for variable 'v'.

Reorder the terms:
25 + -4 + 6v + 4v + 2v2 + -1v2 = 4 + -4v + v2 + -4 + 4v + -1v2

Combine like terms: 25 + -4 = 21
21 + 6v + 4v + 2v2 + -1v2 = 4 + -4v + v2 + -4 + 4v + -1v2

Combine like terms: 6v + 4v = 10v
21 + 10v + 2v2 + -1v2 = 4 + -4v + v2 + -4 + 4v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
21 + 10v + 1v2 = 4 + -4v + v2 + -4 + 4v + -1v2

Reorder the terms:
21 + 10v + 1v2 = 4 + -4 + -4v + 4v + v2 + -1v2

Combine like terms: 4 + -4 = 0
21 + 10v + 1v2 = 0 + -4v + 4v + v2 + -1v2
21 + 10v + 1v2 = -4v + 4v + v2 + -1v2

Combine like terms: -4v + 4v = 0
21 + 10v + 1v2 = 0 + v2 + -1v2
21 + 10v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
21 + 10v + 1v2 = 0

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


Subproblem 1
Set the factor '(7 + v)' equal to zero and attempt to solve:

Simplifying
7 + v = 0

Solving
7 + v = 0

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

Add '-7' to each side of the equation.
7 + -7 + v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + v = 0 + -7
v = 0 + -7

Combine like terms: 0 + -7 = -7
v = -7

Simplifying
v = -7

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 = {-7, -3}

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