4U^2+20UV+9V^2=0

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Solution for 4U^2+20UV+9V^2=0 equation: 


Simplifying
4U2 + 20UV + 9V2 = 0

Reorder the terms:
20UV + 4U2 + 9V2 = 0

Solving
20UV + 4U2 + 9V2 = 0

Solving for variable 'U'.

Factor a trinomial.
(2U + V)(2U + 9V) = 0


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

Simplifying
2U + V = 0

Solving
2U + V = 0

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

Add '-1V' to each side of the equation.
2U + V + -1V = 0 + -1V

Combine like terms: V + -1V = 0
2U + 0 = 0 + -1V
2U = 0 + -1V
Remove the zero:
2U = -1V

Divide each side by '2'.
U = -0.5V

Simplifying
U = -0.5V

Subproblem 2
Set the factor '(2U + 9V)' equal to zero and attempt to solve:

Simplifying
2U + 9V = 0

Solving
2U + 9V = 0

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

Add '-9V' to each side of the equation.
2U + 9V + -9V = 0 + -9V

Combine like terms: 9V + -9V = 0
2U + 0 = 0 + -9V
2U = 0 + -9V
Remove the zero:
2U = -9V

Divide each side by '2'.
U = -4.5V

Simplifying
U = -4.5V
Solution
U = {-0.5V, -4.5V}

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