0=t^2+4t-12

Solution for 0=t^2+4t-12 equation:

Simplifying
0 = t2 + 4t + -12

Reorder the terms:
0 = -12 + 4t + t2

Solving
0 = -12 + 4t + t2

Solving for variable 't'.

Combine like terms: 0 + 12 = 12
12 + -4t + -1t2 = -12 + 4t + t2 + 12 + -4t + -1t2

Reorder the terms:
12 + -4t + -1t2 = -12 + 12 + 4t + -4t + t2 + -1t2

Combine like terms: -12 + 12 = 0
12 + -4t + -1t2 = 0 + 4t + -4t + t2 + -1t2
12 + -4t + -1t2 = 4t + -4t + t2 + -1t2

Combine like terms: 4t + -4t = 0
12 + -4t + -1t2 = 0 + t2 + -1t2
12 + -4t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
12 + -4t + -1t2 = 0

Factor a trinomial.
(2 + -1t)(6 + 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 '(6 + t)' equal to zero and attempt to solve:

Simplifying
6 + t = 0

Solving
6 + t = 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 + t = 0 + -6

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

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

Simplifying
t = -6
Solution
t = {2, -6}