(t-3)(2t+1)=0

Solution for (t-3)(2t+1)=0 equation:

Simplifying
(t + -3)(2t + 1) = 0

Reorder the terms:
(-3 + t)(2t + 1) = 0

Reorder the terms:
(-3 + t)(1 + 2t) = 0

Multiply (-3 + t) * (1 + 2t)
(-3(1 + 2t) + t(1 + 2t)) = 0
((1 * -3 + 2t * -3) + t(1 + 2t)) = 0
((-3 + -6t) + t(1 + 2t)) = 0
(-3 + -6t + (1 * t + 2t * t)) = 0
(-3 + -6t + (1t + 2t2)) = 0

Combine like terms: -6t + 1t = -5t
(-3 + -5t + 2t2) = 0

Solving
-3 + -5t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1 + -2t)(3 + -1t) = 0

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

Simplifying
-1 + -2t = 0

Solving
-1 + -2t = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -2t = 0 + 1
-2t = 0 + 1

Combine like terms: 0 + 1 = 1
-2t = 1

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

Simplifying
t = -0.5
Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

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