v^2+10v+25=2v^2+19v+45

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Solution for v^2+10v+25=2v^2+19v+45 equation: 


Simplifying
v2 + 10v + 25 = 2v2 + 19v + 45

Reorder the terms:
25 + 10v + v2 = 2v2 + 19v + 45

Reorder the terms:
25 + 10v + v2 = 45 + 19v + 2v2

Solving
25 + 10v + v2 = 45 + 19v + 2v2

Solving for variable 'v'.

Reorder the terms:
25 + -45 + 10v + -19v + v2 + -2v2 = 45 + 19v + 2v2 + -45 + -19v + -2v2

Combine like terms: 25 + -45 = -20
-20 + 10v + -19v + v2 + -2v2 = 45 + 19v + 2v2 + -45 + -19v + -2v2

Combine like terms: 10v + -19v = -9v
-20 + -9v + v2 + -2v2 = 45 + 19v + 2v2 + -45 + -19v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-20 + -9v + -1v2 = 45 + 19v + 2v2 + -45 + -19v + -2v2

Reorder the terms:
-20 + -9v + -1v2 = 45 + -45 + 19v + -19v + 2v2 + -2v2

Combine like terms: 45 + -45 = 0
-20 + -9v + -1v2 = 0 + 19v + -19v + 2v2 + -2v2
-20 + -9v + -1v2 = 19v + -19v + 2v2 + -2v2

Combine like terms: 19v + -19v = 0
-20 + -9v + -1v2 = 0 + 2v2 + -2v2
-20 + -9v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-20 + -9v + -1v2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(20 + 9v + v2) = 0

Factor a trinomial.
-1((5 + v)(4 + v)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + v)' equal to zero and attempt to solve:

Simplifying
5 + v = 0

Solving
5 + v = 0

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

Add '-5' to each side of the equation.
5 + -5 + v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + v = 0 + -5
v = 0 + -5

Combine like terms: 0 + -5 = -5
v = -5

Simplifying
v = -5

Subproblem 2
Set the factor '(4 + v)' equal to zero and attempt to solve:

Simplifying
4 + v = 0

Solving
4 + v = 0

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

Add '-4' to each side of the equation.
4 + -4 + v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + v = 0 + -4
v = 0 + -4

Combine like terms: 0 + -4 = -4
v = -4

Simplifying
v = -4
Solution
v = {-5, -4}

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