(3t-8)(t-1)=0

Solution for (3t-8)(t-1)=0 equation:

Simplifying
(3t + -8)(t + -1) = 0

Reorder the terms:
(-8 + 3t)(t + -1) = 0

Reorder the terms:
(-8 + 3t)(-1 + t) = 0

Multiply (-8 + 3t) * (-1 + t)
(-8(-1 + t) + 3t * (-1 + t)) = 0
((-1 * -8 + t * -8) + 3t * (-1 + t)) = 0
((8 + -8t) + 3t * (-1 + t)) = 0
(8 + -8t + (-1 * 3t + t * 3t)) = 0
(8 + -8t + (-3t + 3t2)) = 0

Combine like terms: -8t + -3t = -11t
(8 + -11t + 3t2) = 0

Solving
8 + -11t + 3t2 = 0

Solving for variable 't'.

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

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

Simplifying
1 + -1t = 0

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

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

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

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

Simplifying
t = 1
Subproblem 2
Set the factor '(8 + -3t)' equal to zero and attempt to solve:

Simplifying
8 + -3t = 0

Solving
8 + -3t = 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 + -3t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3t = 0 + -8
-3t = 0 + -8

Combine like terms: 0 + -8 = -8
-3t = -8

Divide each side by '-3'.
t = 2.666666667

Simplifying
t = 2.666666667
Solution
t = {1, 2.666666667}