(2t+uv)(t+3uv)=0

Solution for (2t+uv)(t+3uv)=0 equation:

Simplifying
(2t + uv)(t + 3uv) = 0

Multiply (2t + uv) * (t + 3uv)
(2t * (t + 3uv) + uv(t + 3uv)) = 0
((t * 2t + 3uv * 2t) + uv(t + 3uv)) = 0

Reorder the terms:
((6tuv + 2t2) + uv(t + 3uv)) = 0
((6tuv + 2t2) + uv(t + 3uv)) = 0
(6tuv + 2t2 + (t * uv + 3uv * uv)) = 0
(6tuv + 2t2 + (tuv + 3u2v2)) = 0

Reorder the terms:
(6tuv + tuv + 2t2 + 3u2v2) = 0

Combine like terms: 6tuv + tuv = 7tuv
(7tuv + 2t2 + 3u2v2) = 0

Solving
7tuv + 2t2 + 3u2v2 = 0

Solving for variable 't'.

Factor a trinomial.
(2t + uv)(t + 3uv) = 0

Subproblem 1
Set the factor '(2t + uv)' equal to zero and attempt to solve:

Simplifying
2t + uv = 0

Solving
2t + uv = 0

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

Add '-1uv' to each side of the equation.
2t + uv + -1uv = 0 + -1uv

Combine like terms: uv + -1uv = 0
2t + 0 = 0 + -1uv
2t = 0 + -1uv
Remove the zero:
2t = -1uv

Divide each side by '2'.
t = -0.5uv

Simplifying
t = -0.5uv
Subproblem 2
Set the factor '(t + 3uv)' equal to zero and attempt to solve:

Simplifying
t + 3uv = 0

Solving
t + 3uv = 0

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

Add '-3uv' to each side of the equation.
t + 3uv + -3uv = 0 + -3uv

Combine like terms: 3uv + -3uv = 0
t + 0 = 0 + -3uv
t = 0 + -3uv
Remove the zero:
t = -3uv

Simplifying
t = -3uv
Solution
t = {-0.5uv, -3uv}