(v+5)(v+5)=2v^2+5v+31

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Solution for (v+5)(v+5)=2v^2+5v+31 equation: 


Simplifying
(v + 5)(v + 5) = 2v2 + 5v + 31

Reorder the terms:
(5 + v)(v + 5) = 2v2 + 5v + 31

Reorder the terms:
(5 + v)(5 + v) = 2v2 + 5v + 31

Multiply (5 + v) * (5 + v)
(5(5 + v) + v(5 + v)) = 2v2 + 5v + 31
((5 * 5 + v * 5) + v(5 + v)) = 2v2 + 5v + 31
((25 + 5v) + v(5 + v)) = 2v2 + 5v + 31
(25 + 5v + (5 * v + v * v)) = 2v2 + 5v + 31
(25 + 5v + (5v + v2)) = 2v2 + 5v + 31

Combine like terms: 5v + 5v = 10v
(25 + 10v + v2) = 2v2 + 5v + 31

Reorder the terms:
25 + 10v + v2 = 31 + 5v + 2v2

Solving
25 + 10v + v2 = 31 + 5v + 2v2

Solving for variable 'v'.

Reorder the terms:
25 + -31 + 10v + -5v + v2 + -2v2 = 31 + 5v + 2v2 + -31 + -5v + -2v2

Combine like terms: 25 + -31 = -6
-6 + 10v + -5v + v2 + -2v2 = 31 + 5v + 2v2 + -31 + -5v + -2v2

Combine like terms: 10v + -5v = 5v
-6 + 5v + v2 + -2v2 = 31 + 5v + 2v2 + -31 + -5v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-6 + 5v + -1v2 = 31 + 5v + 2v2 + -31 + -5v + -2v2

Reorder the terms:
-6 + 5v + -1v2 = 31 + -31 + 5v + -5v + 2v2 + -2v2

Combine like terms: 31 + -31 = 0
-6 + 5v + -1v2 = 0 + 5v + -5v + 2v2 + -2v2
-6 + 5v + -1v2 = 5v + -5v + 2v2 + -2v2

Combine like terms: 5v + -5v = 0
-6 + 5v + -1v2 = 0 + 2v2 + -2v2
-6 + 5v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-6 + 5v + -1v2 = 0

Factor a trinomial.
(-3 + v)(2 + -1v) = 0


Subproblem 1
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

Subproblem 2
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
Solution
v = {3, 2}

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