2t^2+t-12=0

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

Simplifying
2t2 + t + -12 = 0

Reorder the terms:
-12 + t + 2t2 = 0

Solving
-12 + t + 2t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-6 + 0.5t + t2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 0.5t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + 0.5t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 0.5t + t2 = 0 + 6
0.5t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
0.5t + t2 = 6

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5t + 0.25 + t2 = 6 + 0.25

Reorder the terms:
0.25 + 0.5t + t2 = 6 + 0.25

Combine like terms: 6 + 0.25 = 6.25
0.25 + 0.5t + t2 = 6.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 6.25

Calculate the square root of the right side: 2.5

Break this problem into two subproblems by setting 
(t + 0.5) equal to 2.5 and -2.5.

Subproblem 1
t + 0.5 = 2.5

Simplifying
t + 0.5 = 2.5

Reorder the terms:
0.5 + t = 2.5

Solving
0.5 + t = 2.5

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 2.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 2.5 + -0.5
t = 2.5 + -0.5

Combine like terms: 2.5 + -0.5 = 2
t = 2

Simplifying
t = 2

Subproblem 2
t + 0.5 = -2.5

Simplifying
t + 0.5 = -2.5

Reorder the terms:
0.5 + t = -2.5

Solving
0.5 + t = -2.5

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -2.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -2.5 + -0.5
t = -2.5 + -0.5

Combine like terms: -2.5 + -0.5 = -3
t = -3

Simplifying
t = -3

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2, -3}