0=10u^2-3uv-4v^2

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Solution for 0=10u^2-3uv-4v^2 equation: 


Simplifying
0 = 10u2 + -3uv + -4v2

Reorder the terms:
0 = -3uv + 10u2 + -4v2

Solving
0 = -3uv + 10u2 + -4v2

Solving for variable 'u'.
Remove the zero:
3uv + -10u2 + 4v2 = -3uv + 10u2 + -4v2 + 3uv + -10u2 + 4v2

Reorder the terms:
3uv + -10u2 + 4v2 = -3uv + 3uv + 10u2 + -10u2 + -4v2 + 4v2

Combine like terms: -3uv + 3uv = 0
3uv + -10u2 + 4v2 = 0 + 10u2 + -10u2 + -4v2 + 4v2
3uv + -10u2 + 4v2 = 10u2 + -10u2 + -4v2 + 4v2

Combine like terms: 10u2 + -10u2 = 0
3uv + -10u2 + 4v2 = 0 + -4v2 + 4v2
3uv + -10u2 + 4v2 = -4v2 + 4v2

Combine like terms: -4v2 + 4v2 = 0
3uv + -10u2 + 4v2 = 0

Factor a trinomial.
(-2u + -1v)(5u + -4v) = 0


Subproblem 1
Set the factor '(-2u + -1v)' equal to zero and attempt to solve:

Simplifying
-2u + -1v = 0

Solving
-2u + -1v = 0

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

Add 'v' to each side of the equation.
-2u + -1v + v = 0 + v

Combine like terms: -1v + v = 0
-2u + 0 = 0 + v
-2u = 0 + v
Remove the zero:
-2u = v

Divide each side by '-2'.
u = -0.5v

Simplifying
u = -0.5v

Subproblem 2
Set the factor '(5u + -4v)' equal to zero and attempt to solve:

Simplifying
5u + -4v = 0

Solving
5u + -4v = 0

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

Add '4v' to each side of the equation.
5u + -4v + 4v = 0 + 4v

Combine like terms: -4v + 4v = 0
5u + 0 = 0 + 4v
5u = 0 + 4v
Remove the zero:
5u = 4v

Divide each side by '5'.
u = 0.8v

Simplifying
u = 0.8v
Solution
u = {-0.5v, 0.8v}

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