t(2t-3u)+u(2t-3u)=

Solution for t(2t-3u)+u(2t-3u)= equation:

Simplifying
t(2t + -3u) + u(2t + -3u) = 0
(2t * t + -3u * t) + u(2t + -3u) = 0

Reorder the terms:
(-3tu + 2t2) + u(2t + -3u) = 0
(-3tu + 2t2) + u(2t + -3u) = 0
-3tu + 2t2 + (2t * u + -3u * u) = 0
-3tu + 2t2 + (2tu + -3u2) = 0

Reorder the terms:
-3tu + 2tu + 2t2 + -3u2 = 0

Combine like terms: -3tu + 2tu = -1tu
-1tu + 2t2 + -3u2 = 0

Solving
-1tu + 2t2 + -3u2 = 0

Solving for variable 't'.

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

Subproblem 1
Set the factor '(2t + -3u)' equal to zero and attempt to solve:

Simplifying
2t + -3u = 0

Solving
2t + -3u = 0

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

Add '3u' to each side of the equation.
2t + -3u + 3u = 0 + 3u

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

Divide each side by '2'.
t = 1.5u

Simplifying
t = 1.5u
Subproblem 2
Set the factor '(t + u)' equal to zero and attempt to solve:

Simplifying
t + u = 0

Solving
t + u = 0

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

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

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

Simplifying
t = -1u
Solution
t = {1.5u, -1u}