(2t-17)(t+4)=0

Solution for (2t-17)(t+4)=0 equation:

Simplifying
(2t + -17)(t + 4) = 0

Reorder the terms:
(-17 + 2t)(t + 4) = 0

Reorder the terms:
(-17 + 2t)(4 + t) = 0

Multiply (-17 + 2t) * (4 + t)
(-17(4 + t) + 2t * (4 + t)) = 0
((4 * -17 + t * -17) + 2t * (4 + t)) = 0
((-68 + -17t) + 2t * (4 + t)) = 0
(-68 + -17t + (4 * 2t + t * 2t)) = 0
(-68 + -17t + (8t + 2t2)) = 0

Combine like terms: -17t + 8t = -9t
(-68 + -9t + 2t2) = 0

Solving
-68 + -9t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-4 + -1t)(17 + -2t) = 0

Subproblem 1
Set the factor '(-4 + -1t)' equal to zero and attempt to solve:

Simplifying
-4 + -1t = 0

Solving
-4 + -1t = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1t = 0 + 4
-1t = 0 + 4

Combine like terms: 0 + 4 = 4
-1t = 4

Divide each side by '-1'.
t = -4

Simplifying
t = -4
Subproblem 2
Set the factor '(17 + -2t)' equal to zero and attempt to solve:

Simplifying
17 + -2t = 0

Solving
17 + -2t = 0

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

Add '-17' to each side of the equation.
17 + -17 + -2t = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -2t = 0 + -17
-2t = 0 + -17

Combine like terms: 0 + -17 = -17
-2t = -17

Divide each side by '-2'.
t = 8.5

Simplifying
t = 8.5
Solution
t = {-4, 8.5}