2v^2+14v+21=v^2+36

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Solution for 2v^2+14v+21=v^2+36 equation: 


Simplifying
2v2 + 14v + 21 = v2 + 36

Reorder the terms:
21 + 14v + 2v2 = v2 + 36

Reorder the terms:
21 + 14v + 2v2 = 36 + v2

Solving
21 + 14v + 2v2 = 36 + v2

Solving for variable 'v'.

Reorder the terms:
21 + -36 + 14v + 2v2 + -1v2 = 36 + v2 + -36 + -1v2

Combine like terms: 21 + -36 = -15
-15 + 14v + 2v2 + -1v2 = 36 + v2 + -36 + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
-15 + 14v + 1v2 = 36 + v2 + -36 + -1v2

Reorder the terms:
-15 + 14v + 1v2 = 36 + -36 + v2 + -1v2

Combine like terms: 36 + -36 = 0
-15 + 14v + 1v2 = 0 + v2 + -1v2
-15 + 14v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
-15 + 14v + 1v2 = 0

Factor a trinomial.
(-15 + -1v)(1 + -1v) = 0


Subproblem 1
Set the factor '(-15 + -1v)' equal to zero and attempt to solve:

Simplifying
-15 + -1v = 0

Solving
-15 + -1v = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1v = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1v = 0 + 15
-1v = 0 + 15

Combine like terms: 0 + 15 = 15
-1v = 15

Divide each side by '-1'.
v = -15

Simplifying
v = -15

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

Simplifying
1 + -1v = 0

Solving
1 + -1v = 0

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

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

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

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

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

Simplifying
v = 1
Solution
v = {-15, 1}

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