0=t^2+t-6

Solution for 0=t^2+t-6 equation:

Simplifying
0 = t2 + t + -6

Reorder the terms:
0 = -6 + t + t2

Solving
0 = -6 + t + t2

Solving for variable 't'.

Combine like terms: 0 + 6 = 6
6 + -1t + -1t2 = -6 + t + t2 + 6 + -1t + -1t2

Reorder the terms:
6 + -1t + -1t2 = -6 + 6 + t + -1t + t2 + -1t2

Combine like terms: -6 + 6 = 0
6 + -1t + -1t2 = 0 + t + -1t + t2 + -1t2
6 + -1t + -1t2 = t + -1t + t2 + -1t2

Combine like terms: t + -1t = 0
6 + -1t + -1t2 = 0 + t2 + -1t2
6 + -1t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
6 + -1t + -1t2 = 0

Factor a trinomial.
(2 + -1t)(3 + t) = 0

Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
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 = {2, -3}