25-16v^2=12v(v+5)

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Solution for 25-16v^2=12v(v+5) equation: 


Simplifying
25 + -16v2 = 12v(v + 5)

Reorder the terms:
25 + -16v2 = 12v(5 + v)
25 + -16v2 = (5 * 12v + v * 12v)
25 + -16v2 = (60v + 12v2)

Solving
25 + -16v2 = 60v + 12v2

Solving for variable 'v'.

Reorder the terms:
25 + -60v + -16v2 + -12v2 = 60v + 12v2 + -60v + -12v2

Combine like terms: -16v2 + -12v2 = -28v2
25 + -60v + -28v2 = 60v + 12v2 + -60v + -12v2

Reorder the terms:
25 + -60v + -28v2 = 60v + -60v + 12v2 + -12v2

Combine like terms: 60v + -60v = 0
25 + -60v + -28v2 = 0 + 12v2 + -12v2
25 + -60v + -28v2 = 12v2 + -12v2

Combine like terms: 12v2 + -12v2 = 0
25 + -60v + -28v2 = 0

Factor a trinomial.
(5 + -14v)(5 + 2v) = 0


Subproblem 1
Set the factor '(5 + -14v)' equal to zero and attempt to solve:

Simplifying
5 + -14v = 0

Solving
5 + -14v = 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 + -14v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -14v = 0 + -5
-14v = 0 + -5

Combine like terms: 0 + -5 = -5
-14v = -5

Divide each side by '-14'.
v = 0.3571428571

Simplifying
v = 0.3571428571

Subproblem 2
Set the factor '(5 + 2v)' equal to zero and attempt to solve:

Simplifying
5 + 2v = 0

Solving
5 + 2v = 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 + 2v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2v = 0 + -5
2v = 0 + -5

Combine like terms: 0 + -5 = -5
2v = -5

Divide each side by '2'.
v = -2.5

Simplifying
v = -2.5
Solution
v = {0.3571428571, -2.5}

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