72u^2+24uv+2v^2=

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Solution for 72u^2+24uv+2v^2= equation: 


Simplifying
72u2 + 24uv + 2v2 = 0

Reorder the terms:
24uv + 72u2 + 2v2 = 0

Solving
24uv + 72u2 + 2v2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12uv + 36u2 + v2) = 0

Factor a trinomial.
2((6u + v)(6u + v)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(6u + v)' equal to zero and attempt to solve:

Simplifying
6u + v = 0

Solving
6u + v = 0

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

Add '-1v' to each side of the equation.
6u + v + -1v = 0 + -1v

Combine like terms: v + -1v = 0
6u + 0 = 0 + -1v
6u = 0 + -1v
Remove the zero:
6u = -1v

Divide each side by '6'.
u = -0.1666666667v

Simplifying
u = -0.1666666667v

Subproblem 2
Set the factor '(6u + v)' equal to zero and attempt to solve:

Simplifying
6u + v = 0

Solving
6u + v = 0

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

Add '-1v' to each side of the equation.
6u + v + -1v = 0 + -1v

Combine like terms: v + -1v = 0
6u + 0 = 0 + -1v
6u = 0 + -1v
Remove the zero:
6u = -1v

Divide each side by '6'.
u = -0.1666666667v

Simplifying
u = -0.1666666667v
Solution
u = {-0.1666666667v, -0.1666666667v}

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