5v^2+11v+14=v-7+4v^2

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Solution for 5v^2+11v+14=v-7+4v^2 equation: 


Simplifying
5v2 + 11v + 14 = v + -7 + 4v2

Reorder the terms:
14 + 11v + 5v2 = v + -7 + 4v2

Reorder the terms:
14 + 11v + 5v2 = -7 + v + 4v2

Solving
14 + 11v + 5v2 = -7 + v + 4v2

Solving for variable 'v'.

Reorder the terms:
14 + 7 + 11v + -1v + 5v2 + -4v2 = -7 + v + 4v2 + 7 + -1v + -4v2

Combine like terms: 14 + 7 = 21
21 + 11v + -1v + 5v2 + -4v2 = -7 + v + 4v2 + 7 + -1v + -4v2

Combine like terms: 11v + -1v = 10v
21 + 10v + 5v2 + -4v2 = -7 + v + 4v2 + 7 + -1v + -4v2

Combine like terms: 5v2 + -4v2 = 1v2
21 + 10v + 1v2 = -7 + v + 4v2 + 7 + -1v + -4v2

Reorder the terms:
21 + 10v + 1v2 = -7 + 7 + v + -1v + 4v2 + -4v2

Combine like terms: -7 + 7 = 0
21 + 10v + 1v2 = 0 + v + -1v + 4v2 + -4v2
21 + 10v + 1v2 = v + -1v + 4v2 + -4v2

Combine like terms: v + -1v = 0
21 + 10v + 1v2 = 0 + 4v2 + -4v2
21 + 10v + 1v2 = 4v2 + -4v2

Combine like terms: 4v2 + -4v2 = 0
21 + 10v + 1v2 = 0

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


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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