3u^2+10uv-8v^2=

Solution for 3u^2+10uv-8v^2= equation:

Simplifying
3u2 + 10uv + -8v2 = 0

Reorder the terms:
10uv + 3u2 + -8v2 = 0

Solving
10uv + 3u2 + -8v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(3u + -2v)(u + 4v) = 0

Subproblem 1
Set the factor '(3u + -2v)' equal to zero and attempt to solve:

Simplifying
3u + -2v = 0

Solving
3u + -2v = 0

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

Add '2v' to each side of the equation.
3u + -2v + 2v = 0 + 2v

Combine like terms: -2v + 2v = 0
3u + 0 = 0 + 2v
3u = 0 + 2v
Remove the zero:
3u = 2v

Divide each side by '3'.
u = 0.6666666667v

Simplifying
u = 0.6666666667v
Subproblem 2
Set the factor '(u + 4v)' equal to zero and attempt to solve:

Simplifying
u + 4v = 0

Solving
u + 4v = 0

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

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

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

Simplifying
u = -4v
Solution
u = {0.6666666667v, -4v}