(t-8)(t-5)=0

Solution for (t-8)(t-5)=0 equation:

Simplifying
(t + -8)(t + -5) = 0

Reorder the terms:
(-8 + t)(t + -5) = 0

Reorder the terms:
(-8 + t)(-5 + t) = 0

Multiply (-8 + t) * (-5 + t)
(-8(-5 + t) + t(-5 + t)) = 0
((-5 * -8 + t * -8) + t(-5 + t)) = 0
((40 + -8t) + t(-5 + t)) = 0
(40 + -8t + (-5 * t + t * t)) = 0
(40 + -8t + (-5t + t2)) = 0

Combine like terms: -8t + -5t = -13t
(40 + -13t + t2) = 0

Solving
40 + -13t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(5 + -1t)(8 + -1t) = 0

Subproblem 1
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 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 = {5, 8}