T^2+7T-78=0

Solution for T^2+7T-78=0 equation:

Simplifying
T2 + 7T + -78 = 0

Reorder the terms:
-78 + 7T + T2 = 0

Solving
-78 + 7T + T2 = 0

Solving for variable 'T'.

Factor a trinomial.
(-13 + -1T)(6 + -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 '(6 + -1T)' equal to zero and attempt to solve:

Simplifying
6 + -1T = 0

Solving
6 + -1T = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1T = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1T = 0 + -6
-1T = 0 + -6

Combine like terms: 0 + -6 = -6
-1T = -6

Divide each side by '-1'.
T = 6

Simplifying
T = 6
Solution
T = {-13, 6}