-t^2+10t+39=0

Solution for -t^2+10t+39=0 equation:

Simplifying
-1t2 + 10t + 39 = 0

Reorder the terms:
39 + 10t + -1t2 = 0

Solving
39 + 10t + -1t2 = 0

Solving for variable 't'.

Factor a trinomial.
(13 + -1t)(3 + t) = 0

Subproblem 1
Set the factor '(13 + -1t)' equal to zero and attempt to solve:

Simplifying
13 + -1t = 0

Solving
13 + -1t = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1t = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1t = 0 + -13
-1t = 0 + -13

Combine like terms: 0 + -13 = -13
-1t = -13

Divide each side by '-1'.
t = 13

Simplifying
t = 13
Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 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 + t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t = 0 + -3
t = 0 + -3

Combine like terms: 0 + -3 = -3
t = -3

Simplifying
t = -3
Solution
t = {13, -3}