t^2+12t-32=0

Solution for t^2+12t-32=0 equation:

Simplifying
t2 + 12t + -32 = 0

Reorder the terms:
-32 + 12t + t2 = 0

Solving
-32 + 12t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 12t + 32 + t2 = 0 + 32

Reorder the terms:
-32 + 32 + 12t + t2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 12t + t2 = 0 + 32
12t + t2 = 0 + 32

Combine like terms: 0 + 32 = 32
12t + t2 = 32

The t term is 12t.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12t + 36 + t2 = 32 + 36

Reorder the terms:
36 + 12t + t2 = 32 + 36

Combine like terms: 32 + 36 = 68
36 + 12t + t2 = 68

Factor a perfect square on the left side:
(t + 6)(t + 6) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(t + 6) equal to 8.246211251 and -8.246211251.

Subproblem 1
t + 6 = 8.246211251

Simplifying
t + 6 = 8.246211251

Reorder the terms:
6 + t = 8.246211251

Solving
6 + t = 8.246211251

Solving for variable 't'.

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 = 8.246211251 + -6

Combine like terms: 6 + -6 = 0
0 + t = 8.246211251 + -6
t = 8.246211251 + -6

Combine like terms: 8.246211251 + -6 = 2.246211251
t = 2.246211251

Simplifying
t = 2.246211251

Subproblem 2
t + 6 = -8.246211251

Simplifying
t + 6 = -8.246211251

Reorder the terms:
6 + t = -8.246211251

Solving
6 + t = -8.246211251

Solving for variable 't'.

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 = -8.246211251 + -6

Combine like terms: 6 + -6 = 0
0 + t = -8.246211251 + -6
t = -8.246211251 + -6

Combine like terms: -8.246211251 + -6 = -14.246211251
t = -14.246211251

Simplifying
t = -14.246211251

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.246211251, -14.246211251}