2t^2+4t-12=0

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

Simplifying
2t2 + 4t + -12 = 0

Reorder the terms:
-12 + 4t + 2t2 = 0

Solving
-12 + 4t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 2t + t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 2t + t2)' equal to zero and attempt to solve:

Simplifying
-6 + 2t + t2 = 0

Solving
-6 + 2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 2t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + 2t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 2t + t2 = 0 + 6
2t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
2t + t2 = 6

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 6 + 1

Reorder the terms:
1 + 2t + t2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + 2t + t2 = 7

Factor a perfect square on the left side:
(t + 1)(t + 1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(t + 1) equal to 2.645751311 and -2.645751311.

Subproblem 1
t + 1 = 2.645751311

Simplifying
t + 1 = 2.645751311

Reorder the terms:
1 + t = 2.645751311

Solving
1 + t = 2.645751311

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + t = 2.645751311 + -1
t = 2.645751311 + -1

Combine like terms: 2.645751311 + -1 = 1.645751311
t = 1.645751311

Simplifying
t = 1.645751311

Subproblem 2
t + 1 = -2.645751311

Simplifying
t + 1 = -2.645751311

Reorder the terms:
1 + t = -2.645751311

Solving
1 + t = -2.645751311

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + t = -2.645751311 + -1
t = -2.645751311 + -1

Combine like terms: -2.645751311 + -1 = -3.645751311
t = -3.645751311

Simplifying
t = -3.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.645751311, -3.645751311}
Solution
t = {1.645751311, -3.645751311}