(-t-6)-(t^2+3t-4)=

Solution for (-t-6)-(t^2+3t-4)= equation:

Simplifying
(-1t + -6) + -1(t2 + 3t + -4) = 0

Reorder the terms:
(-6 + -1t) + -1(t2 + 3t + -4) = 0

Remove parenthesis around (-6 + -1t)
-6 + -1t + -1(t2 + 3t + -4) = 0

Reorder the terms:
-6 + -1t + -1(-4 + 3t + t2) = 0
-6 + -1t + (-4 * -1 + 3t * -1 + t2 * -1) = 0
-6 + -1t + (4 + -3t + -1t2) = 0

Reorder the terms:
-6 + 4 + -1t + -3t + -1t2 = 0

Combine like terms: -6 + 4 = -2
-2 + -1t + -3t + -1t2 = 0

Combine like terms: -1t + -3t = -4t
-2 + -4t + -1t2 = 0

Solving
-2 + -4t + -1t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 4t + t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 4t + t2)' equal to zero and attempt to solve:

Simplifying
2 + 4t + t2 = 0

Solving
2 + 4t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 4t + -2 + t2 = 0 + -2

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

Combine like terms: 2 + -2 = 0
0 + 4t + t2 = 0 + -2
4t + t2 = 0 + -2

Combine like terms: 0 + -2 = -2
4t + t2 = -2

The t term is 4t.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4t + 4 + t2 = -2 + 4

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

Combine like terms: -2 + 4 = 2
4 + 4t + t2 = 2

Factor a perfect square on the left side:
(t + 2)(t + 2) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(t + 2) equal to 1.414213562 and -1.414213562.

Subproblem 1
t + 2 = 1.414213562

Simplifying
t + 2 = 1.414213562

Reorder the terms:
2 + t = 1.414213562

Solving
2 + t = 1.414213562

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = 1.414213562 + -2

Combine like terms: 2 + -2 = 0
0 + t = 1.414213562 + -2
t = 1.414213562 + -2

Combine like terms: 1.414213562 + -2 = -0.585786438
t = -0.585786438

Simplifying
t = -0.585786438

Subproblem 2
t + 2 = -1.414213562

Simplifying
t + 2 = -1.414213562

Reorder the terms:
2 + t = -1.414213562

Solving
2 + t = -1.414213562

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = -1.414213562 + -2

Combine like terms: 2 + -2 = 0
0 + t = -1.414213562 + -2
t = -1.414213562 + -2

Combine like terms: -1.414213562 + -2 = -3.414213562
t = -3.414213562

Simplifying
t = -3.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.585786438, -3.414213562}
Solution
t = {-0.585786438, -3.414213562}