0=t^2-t-12

Solution for 0=t^2-t-12 equation:

Simplifying
0 = t2 + -1t + -12

Reorder the terms:
0 = -12 + -1t + t2

Solving
0 = -12 + -1t + t2

Solving for variable 't'.

Combine like terms: 0 + 12 = 12
12 + t + -1t2 = -12 + -1t + t2 + 12 + t + -1t2

Reorder the terms:
12 + t + -1t2 = -12 + 12 + -1t + t + t2 + -1t2

Combine like terms: -12 + 12 = 0
12 + t + -1t2 = 0 + -1t + t + t2 + -1t2
12 + t + -1t2 = -1t + t + t2 + -1t2

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

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

Factor a trinomial.
(4 + -1t)(3 + t) = 0

Subproblem 1
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
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 = {4, -3}