15u^2-7uv-4v^2=

Solution for 15u^2-7uv-4v^2= equation:

Simplifying
15u2 + -7uv + -4v2 = 0

Reorder the terms:
-7uv + 15u2 + -4v2 = 0

Solving
-7uv + 15u2 + -4v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(5u + -4v)(3u + v) = 0

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

Simplifying
3u + v = 0

Solving
3u + v = 0

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

Add '-1v' to each side of the equation.
3u + v + -1v = 0 + -1v

Combine like terms: v + -1v = 0
3u + 0 = 0 + -1v
3u = 0 + -1v
Remove the zero:
3u = -1v

Divide each side by '3'.
u = -0.3333333333v

Simplifying
u = -0.3333333333v
Solution
u = {0.8v, -0.3333333333v}