2t^2+t(-3)=0

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

Simplifying
2t2 + t(-3) = 0

Reorder the terms for easier multiplication:
2t2 + -3t = 0

Reorder the terms:
-3t + 2t2 = 0

Solving
-3t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-3 + 2t) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(-3 + 2t)' equal to zero and attempt to solve:

Simplifying
-3 + 2t = 0

Solving
-3 + 2t = 0

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

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

Combine like terms: -3 + 3 = 0
0 + 2t = 0 + 3
2t = 0 + 3

Combine like terms: 0 + 3 = 3
2t = 3

Divide each side by '2'.
t = 1.5

Simplifying
t = 1.5
Solution
t = {0, 1.5}