t[t+1]-4[t+2]=

Solution for t[t+1]-4[t+2]= equation:

Simplifying
t[t + 1] + -4[t + 2] = 0

Reorder the terms:
t[1 + t] + -4[t + 2] = 0
[1 * t + t * t] + -4[t + 2] = 0
[1t + t2] + -4[t + 2] = 0

Reorder the terms:
1t + t2 + -4[2 + t] = 0
1t + t2 + [2 * -4 + t * -4] = 0
1t + t2 + [-8 + -4t] = 0

Reorder the terms:
-8 + 1t + -4t + t2 = 0

Combine like terms: 1t + -4t = -3t
-8 + -3t + t2 = 0

Solving
-8 + -3t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -3t + 8 + t2 = 0 + 8

Reorder the terms:
-8 + 8 + -3t + t2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3t + t2 = 0 + 8
-3t + t2 = 0 + 8

Combine like terms: 0 + 8 = 8
-3t + t2 = 8

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = 8 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 8 + 2.25

Combine like terms: 8 + 2.25 = 10.25
2.25 + -3t + t2 = 10.25

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(t + -1.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
t + -1.5 = 3.201562119

Simplifying
t + -1.5 = 3.201562119

Reorder the terms:
-1.5 + t = 3.201562119

Solving
-1.5 + t = 3.201562119

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 3.201562119 + 1.5
t = 3.201562119 + 1.5

Combine like terms: 3.201562119 + 1.5 = 4.701562119
t = 4.701562119

Simplifying
t = 4.701562119

Subproblem 2
t + -1.5 = -3.201562119

Simplifying
t + -1.5 = -3.201562119

Reorder the terms:
-1.5 + t = -3.201562119

Solving
-1.5 + t = -3.201562119

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -3.201562119 + 1.5
t = -3.201562119 + 1.5

Combine like terms: -3.201562119 + 1.5 = -1.701562119
t = -1.701562119

Simplifying
t = -1.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.701562119, -1.701562119}