t^2+10t=39

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

Simplifying
t2 + 10t = 39

Reorder the terms:
10t + t2 = 39

Solving
10t + t2 = 39

Solving for variable 't'.

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

Combine like terms: 39 + -39 = 0
-39 + 10t + t2 = 0

Factor a trinomial.
(-13 + -1t)(3 + -1t) = 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 + -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
Solution
t = {-13, 3}