(4u+9v)(4u+9v)=0

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Solution for (4u+9v)(4u+9v)=0 equation: 


Simplifying
(4u + 9v)(4u + 9v) = 0

Multiply (4u + 9v) * (4u + 9v)
(4u * (4u + 9v) + 9v * (4u + 9v)) = 0
((4u * 4u + 9v * 4u) + 9v * (4u + 9v)) = 0

Reorder the terms:
((36uv + 16u2) + 9v * (4u + 9v)) = 0
((36uv + 16u2) + 9v * (4u + 9v)) = 0
(36uv + 16u2 + (4u * 9v + 9v * 9v)) = 0
(36uv + 16u2 + (36uv + 81v2)) = 0

Reorder the terms:
(36uv + 36uv + 16u2 + 81v2) = 0

Combine like terms: 36uv + 36uv = 72uv
(72uv + 16u2 + 81v2) = 0

Solving
72uv + 16u2 + 81v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(4u + 9v)(4u + 9v) = 0


Subproblem 1
Set the factor '(4u + 9v)' equal to zero and attempt to solve:

Simplifying
4u + 9v = 0

Solving
4u + 9v = 0

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

Add '-9v' to each side of the equation.
4u + 9v + -9v = 0 + -9v

Combine like terms: 9v + -9v = 0
4u + 0 = 0 + -9v
4u = 0 + -9v
Remove the zero:
4u = -9v

Divide each side by '4'.
u = -2.25v

Simplifying
u = -2.25v

Subproblem 2
Set the factor '(4u + 9v)' equal to zero and attempt to solve:

Simplifying
4u + 9v = 0

Solving
4u + 9v = 0

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

Add '-9v' to each side of the equation.
4u + 9v + -9v = 0 + -9v

Combine like terms: 9v + -9v = 0
4u + 0 = 0 + -9v
4u = 0 + -9v
Remove the zero:
4u = -9v

Divide each side by '4'.
u = -2.25v

Simplifying
u = -2.25v
Solution
u = {-2.25v, -2.25v}

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