6=-3t^2+9t-.75

Solution for 6=-3t^2+9t-.75 equation:

Simplifying
6 = -3t2 + 9t + -0.75

Reorder the terms:
6 = -0.75 + 9t + -3t2

Solving
6 = -0.75 + 9t + -3t2

Solving for variable 't'.

Combine like terms: 6 + 0.75 = 6.75
6.75 + -9t + 3t2 = -0.75 + 9t + -3t2 + 0.75 + -9t + 3t2

Reorder the terms:
6.75 + -9t + 3t2 = -0.75 + 0.75 + 9t + -9t + -3t2 + 3t2

Combine like terms: -0.75 + 0.75 = 0.00
6.75 + -9t + 3t2 = 0.00 + 9t + -9t + -3t2 + 3t2
6.75 + -9t + 3t2 = 9t + -9t + -3t2 + 3t2

Combine like terms: 9t + -9t = 0
6.75 + -9t + 3t2 = 0 + -3t2 + 3t2
6.75 + -9t + 3t2 = -3t2 + 3t2

Combine like terms: -3t2 + 3t2 = 0
6.75 + -9t + 3t2 = 0

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

Divide each side by '3'.
2.25 + -3t + t2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -3t + -2.25 + t2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -3t + t2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -3t + t2 = 0 + -2.25
-3t + t2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-3t + t2 = -2.25

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 = -2.25 + 2.25

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

Combine like terms: -2.25 + 2.25 = 0.00
2.25 + -3t + t2 = 0.00

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(t + -1.5) equal to 0.00 and 0.00.

Subproblem 1
t + -1.5 = 0.00

Simplifying
t + -1.5 = 0.00

Reorder the terms:
-1.5 + t = 0.00

Solving
-1.5 + t = 0.00

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 = 0.00 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 0.00 + 1.5
t = 0.00 + 1.5

Combine like terms: 0.00 + 1.5 = 1.5
t = 1.5

Simplifying
t = 1.5

Subproblem 2
t + -1.5 = 0.00

Simplifying
t + -1.5 = 0.00

Reorder the terms:
-1.5 + t = 0.00

Solving
-1.5 + t = 0.00

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 = 0.00 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 0.00 + 1.5
t = 0.00 + 1.5

Combine like terms: 0.00 + 1.5 = 1.5
t = 1.5

Simplifying
t = 1.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.5, 1.5}