v^2+9=2v^2+15v+23

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Solution for v^2+9=2v^2+15v+23 equation: 


Simplifying
v2 + 9 = 2v2 + 15v + 23

Reorder the terms:
9 + v2 = 2v2 + 15v + 23

Reorder the terms:
9 + v2 = 23 + 15v + 2v2

Solving
9 + v2 = 23 + 15v + 2v2

Solving for variable 'v'.

Reorder the terms:
9 + -23 + -15v + v2 + -2v2 = 23 + 15v + 2v2 + -23 + -15v + -2v2

Combine like terms: 9 + -23 = -14
-14 + -15v + v2 + -2v2 = 23 + 15v + 2v2 + -23 + -15v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-14 + -15v + -1v2 = 23 + 15v + 2v2 + -23 + -15v + -2v2

Reorder the terms:
-14 + -15v + -1v2 = 23 + -23 + 15v + -15v + 2v2 + -2v2

Combine like terms: 23 + -23 = 0
-14 + -15v + -1v2 = 0 + 15v + -15v + 2v2 + -2v2
-14 + -15v + -1v2 = 15v + -15v + 2v2 + -2v2

Combine like terms: 15v + -15v = 0
-14 + -15v + -1v2 = 0 + 2v2 + -2v2
-14 + -15v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-14 + -15v + -1v2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 15v + v2) = 0

Factor a trinomial.
-1((14 + v)(1 + v)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(14 + v)' equal to zero and attempt to solve:

Simplifying
14 + v = 0

Solving
14 + v = 0

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

Add '-14' to each side of the equation.
14 + -14 + v = 0 + -14

Combine like terms: 14 + -14 = 0
0 + v = 0 + -14
v = 0 + -14

Combine like terms: 0 + -14 = -14
v = -14

Simplifying
v = -14

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

Simplifying
1 + v = 0

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

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

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

Simplifying
v = -1
Solution
v = {-14, -1}

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