(2t+3)(t-8)=0

Solution for (2t+3)(t-8)=0 equation:

Simplifying
(2t + 3)(t + -8) = 0

Reorder the terms:
(3 + 2t)(t + -8) = 0

Reorder the terms:
(3 + 2t)(-8 + t) = 0

Multiply (3 + 2t) * (-8 + t)
(3(-8 + t) + 2t * (-8 + t)) = 0
((-8 * 3 + t * 3) + 2t * (-8 + t)) = 0
((-24 + 3t) + 2t * (-8 + t)) = 0
(-24 + 3t + (-8 * 2t + t * 2t)) = 0
(-24 + 3t + (-16t + 2t2)) = 0

Combine like terms: 3t + -16t = -13t
(-24 + -13t + 2t2) = 0

Solving
-24 + -13t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-3 + -2t)(8 + -1t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8 + -1t)' equal to zero and attempt to solve:

Simplifying
8 + -1t = 0

Solving
8 + -1t = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1t = 0 + -8
-1t = 0 + -8

Combine like terms: 0 + -8 = -8
-1t = -8

Divide each side by '-1'.
t = 8

Simplifying
t = 8
Solution
t = {-1.5, 8}