(2t-3)(t+6)=0

Solution for (2t-3)(t+6)=0 equation:

Simplifying
(2t + -3)(t + 6) = 0

Reorder the terms:
(-3 + 2t)(t + 6) = 0

Reorder the terms:
(-3 + 2t)(6 + t) = 0

Multiply (-3 + 2t) * (6 + t)
(-3(6 + t) + 2t * (6 + t)) = 0
((6 * -3 + t * -3) + 2t * (6 + t)) = 0
((-18 + -3t) + 2t * (6 + t)) = 0
(-18 + -3t + (6 * 2t + t * 2t)) = 0
(-18 + -3t + (12t + 2t2)) = 0

Combine like terms: -3t + 12t = 9t
(-18 + 9t + 2t2) = 0

Solving
-18 + 9t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-6 + -1t)(3 + -2t) = 0

Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
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 = {-6, 1.5}