-6=-3t^2+9t-.075

Solution for -6=-3t^2+9t-.075 equation:

Simplifying
-6 = -3t2 + 9t + -0.075

Reorder the terms:
-6 = -0.075 + 9t + -3t2

Solving
-6 = -0.075 + 9t + -3t2

Solving for variable 't'.

Combine like terms: -6 + 0.075 = -5.925
-5.925 + -9t + 3t2 = -0.075 + 9t + -3t2 + 0.075 + -9t + 3t2

Reorder the terms:
-5.925 + -9t + 3t2 = -0.075 + 0.075 + 9t + -9t + -3t2 + 3t2

Combine like terms: -0.075 + 0.075 = 0.000
-5.925 + -9t + 3t2 = 0.000 + 9t + -9t + -3t2 + 3t2
-5.925 + -9t + 3t2 = 9t + -9t + -3t2 + 3t2

Combine like terms: 9t + -9t = 0
-5.925 + -9t + 3t2 = 0 + -3t2 + 3t2
-5.925 + -9t + 3t2 = -3t2 + 3t2

Combine like terms: -3t2 + 3t2 = 0
-5.925 + -9t + 3t2 = 0

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

Divide each side by '3'.
-1.975 + -3t + t2 = 0

Move the constant term to the right:

Add '1.975' to each side of the equation.
-1.975 + -3t + 1.975 + t2 = 0 + 1.975

Reorder the terms:
-1.975 + 1.975 + -3t + t2 = 0 + 1.975

Combine like terms: -1.975 + 1.975 = 0.000
0.000 + -3t + t2 = 0 + 1.975
-3t + t2 = 0 + 1.975

Combine like terms: 0 + 1.975 = 1.975
-3t + t2 = 1.975

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 = 1.975 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 1.975 + 2.25

Combine like terms: 1.975 + 2.25 = 4.225
2.25 + -3t + t2 = 4.225

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 4.225

Calculate the square root of the right side: 2.055480479

Break this problem into two subproblems by setting 
(t + -1.5) equal to 2.055480479 and -2.055480479.

Subproblem 1
t + -1.5 = 2.055480479

Simplifying
t + -1.5 = 2.055480479

Reorder the terms:
-1.5 + t = 2.055480479

Solving
-1.5 + t = 2.055480479

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 = 2.055480479 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 2.055480479 + 1.5
t = 2.055480479 + 1.5

Combine like terms: 2.055480479 + 1.5 = 3.555480479
t = 3.555480479

Simplifying
t = 3.555480479

Subproblem 2
t + -1.5 = -2.055480479

Simplifying
t + -1.5 = -2.055480479

Reorder the terms:
-1.5 + t = -2.055480479

Solving
-1.5 + t = -2.055480479

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 = -2.055480479 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -2.055480479 + 1.5
t = -2.055480479 + 1.5

Combine like terms: -2.055480479 + 1.5 = -0.555480479
t = -0.555480479

Simplifying
t = -0.555480479

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.555480479, -0.555480479}