-t^2+14t-45=0

Solution for -t^2+14t-45=0 equation:

Simplifying
-1t2 + 14t + -45 = 0

Reorder the terms:
-45 + 14t + -1t2 = 0

Solving
-45 + 14t + -1t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-9 + t)(5 + -1t) = 0

Subproblem 1
Set the factor '(-9 + t)' equal to zero and attempt to solve:

Simplifying
-9 + t = 0

Solving
-9 + t = 0

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

Add '9' to each side of the equation.
-9 + 9 + t = 0 + 9

Combine like terms: -9 + 9 = 0
0 + t = 0 + 9
t = 0 + 9

Combine like terms: 0 + 9 = 9
t = 9

Simplifying
t = 9
Subproblem 2
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
Solution
t = {9, 5}