170=-t^2+17t+140

Solution for 170=-t^2+17t+140 equation:

Simplifying
170 = -1t2 + 17t + 140

Reorder the terms:
170 = 140 + 17t + -1t2

Solving
170 = 140 + 17t + -1t2

Solving for variable 't'.

Combine like terms: 170 + -140 = 30
30 + -17t + t2 = 140 + 17t + -1t2 + -140 + -17t + t2

Reorder the terms:
30 + -17t + t2 = 140 + -140 + 17t + -17t + -1t2 + t2

Combine like terms: 140 + -140 = 0
30 + -17t + t2 = 0 + 17t + -17t + -1t2 + t2
30 + -17t + t2 = 17t + -17t + -1t2 + t2

Combine like terms: 17t + -17t = 0
30 + -17t + t2 = 0 + -1t2 + t2
30 + -17t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
30 + -17t + t2 = 0

Factor a trinomial.
(2 + -1t)(15 + -1t) = 0

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Subproblem 2
Set the factor '(15 + -1t)' equal to zero and attempt to solve:

Simplifying
15 + -1t = 0

Solving
15 + -1t = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1t = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1t = 0 + -15
-1t = 0 + -15

Combine like terms: 0 + -15 = -15
-1t = -15

Divide each side by '-1'.
t = 15

Simplifying
t = 15
Solution
t = {2, 15}