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

Solution for 17(t-3)(t-8)=0 equation:

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

Reorder the terms:
17(-3 + t)(t + -8) = 0

Reorder the terms:
17(-3 + t)(-8 + t) = 0

Multiply (-3 + t) * (-8 + t)
17(-3(-8 + t) + t(-8 + t)) = 0
17((-8 * -3 + t * -3) + t(-8 + t)) = 0
17((24 + -3t) + t(-8 + t)) = 0
17(24 + -3t + (-8 * t + t * t)) = 0
17(24 + -3t + (-8t + t2)) = 0

Combine like terms: -3t + -8t = -11t
17(24 + -11t + t2) = 0
(24 * 17 + -11t * 17 + t2 * 17) = 0
(408 + -187t + 17t2) = 0

Solving
408 + -187t + 17t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '17'.
17(24 + -11t + t2) = 0

Factor a trinomial.
17((3 + -1t)(8 + -1t)) = 0

Ignore the factor 17.
Subproblem 1
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
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 = {3, 8}