0=t^2-52t-1440

Solution for 0=t^2-52t-1440 equation:

Simplifying
0 = t2 + -52t + -1440

Reorder the terms:
0 = -1440 + -52t + t2

Solving
0 = -1440 + -52t + t2

Solving for variable 't'.

Combine like terms: 0 + 1440 = 1440
1440 + 52t + -1t2 = -1440 + -52t + t2 + 1440 + 52t + -1t2

Reorder the terms:
1440 + 52t + -1t2 = -1440 + 1440 + -52t + 52t + t2 + -1t2

Combine like terms: -1440 + 1440 = 0
1440 + 52t + -1t2 = 0 + -52t + 52t + t2 + -1t2
1440 + 52t + -1t2 = -52t + 52t + t2 + -1t2

Combine like terms: -52t + 52t = 0
1440 + 52t + -1t2 = 0 + t2 + -1t2
1440 + 52t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
1440 + 52t + -1t2 = 0

Factor a trinomial.
(72 + -1t)(20 + t) = 0

Subproblem 1
Set the factor '(72 + -1t)' equal to zero and attempt to solve:

Simplifying
72 + -1t = 0

Solving
72 + -1t = 0

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

Add '-72' to each side of the equation.
72 + -72 + -1t = 0 + -72

Combine like terms: 72 + -72 = 0
0 + -1t = 0 + -72
-1t = 0 + -72

Combine like terms: 0 + -72 = -72
-1t = -72

Divide each side by '-1'.
t = 72

Simplifying
t = 72
Subproblem 2
Set the factor '(20 + t)' equal to zero and attempt to solve:

Simplifying
20 + t = 0

Solving
20 + t = 0

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

Add '-20' to each side of the equation.
20 + -20 + t = 0 + -20

Combine like terms: 20 + -20 = 0
0 + t = 0 + -20
t = 0 + -20

Combine like terms: 0 + -20 = -20
t = -20

Simplifying
t = -20
Solution
t = {72, -20}