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

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


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

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

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

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

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

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

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

Solving for variable 'v'.

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

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

Combine like terms: 4v + 6v = 10v
-21 + 10v + v2 + -2v2 = 25 + -6v + 2v2 + -25 + 6v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-21 + 10v + -1v2 = 25 + -6v + 2v2 + -25 + 6v + -2v2

Reorder the terms:
-21 + 10v + -1v2 = 25 + -25 + -6v + 6v + 2v2 + -2v2

Combine like terms: 25 + -25 = 0
-21 + 10v + -1v2 = 0 + -6v + 6v + 2v2 + -2v2
-21 + 10v + -1v2 = -6v + 6v + 2v2 + -2v2

Combine like terms: -6v + 6v = 0
-21 + 10v + -1v2 = 0 + 2v2 + -2v2
-21 + 10v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-21 + 10v + -1v2 = 0

Factor a trinomial.
(-7 + v)(3 + -1v) = 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 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 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 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Solution
v = {7, 3}

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