0=t^2-t-56

Solution for 0=t^2-t-56 equation:

Simplifying
0 = t2 + -1t + -56

Reorder the terms:
0 = -56 + -1t + t2

Solving
0 = -56 + -1t + t2

Solving for variable 't'.

Combine like terms: 0 + 56 = 56
56 + t + -1t2 = -56 + -1t + t2 + 56 + t + -1t2

Reorder the terms:
56 + t + -1t2 = -56 + 56 + -1t + t + t2 + -1t2

Combine like terms: -56 + 56 = 0
56 + t + -1t2 = 0 + -1t + t + t2 + -1t2
56 + t + -1t2 = -1t + t + t2 + -1t2

Combine like terms: -1t + t = 0
56 + t + -1t2 = 0 + t2 + -1t2
56 + t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
56 + t + -1t2 = 0

Factor a trinomial.
(8 + -1t)(7 + t) = 0

Subproblem 1
Set the factor '(8 + -1t)' equal to zero and attempt to solve:

Simplifying
8 + -1t = 0

Solving
8 + -1t = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1t = 0 + -8
-1t = 0 + -8

Combine like terms: 0 + -8 = -8
-1t = -8

Divide each side by '-1'.
t = 8

Simplifying
t = 8
Subproblem 2
Set the factor '(7 + t)' equal to zero and attempt to solve:

Simplifying
7 + t = 0

Solving
7 + t = 0

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

Add '-7' to each side of the equation.
7 + -7 + t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + t = 0 + -7
t = 0 + -7

Combine like terms: 0 + -7 = -7
t = -7

Simplifying
t = -7
Solution
t = {8, -7}