v^2=2v^2+10v+21

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Solution for v^2=2v^2+10v+21 equation: 


Simplifying
v2 = 2v2 + 10v + 21

Reorder the terms:
v2 = 21 + 10v + 2v2

Solving
v2 = 21 + 10v + 2v2

Solving for variable 'v'.

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 10v + v2) = 0

Factor a trinomial.
-1((7 + v)(3 + v)) = 0

Ignore the factor -1.

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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