v^2+10v+25=2v^2-50

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Solution for v^2+10v+25=2v^2-50 equation: 


Simplifying
v2 + 10v + 25 = 2v2 + -50

Reorder the terms:
25 + 10v + v2 = 2v2 + -50

Reorder the terms:
25 + 10v + v2 = -50 + 2v2

Solving
25 + 10v + v2 = -50 + 2v2

Solving for variable 'v'.

Reorder the terms:
25 + 50 + 10v + v2 + -2v2 = -50 + 2v2 + 50 + -2v2

Combine like terms: 25 + 50 = 75
75 + 10v + v2 + -2v2 = -50 + 2v2 + 50 + -2v2

Combine like terms: v2 + -2v2 = -1v2
75 + 10v + -1v2 = -50 + 2v2 + 50 + -2v2

Reorder the terms:
75 + 10v + -1v2 = -50 + 50 + 2v2 + -2v2

Combine like terms: -50 + 50 = 0
75 + 10v + -1v2 = 0 + 2v2 + -2v2
75 + 10v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
75 + 10v + -1v2 = 0

Factor a trinomial.
(15 + -1v)(5 + v) = 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 '(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
Solution
v = {15, -5}

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