-66t^2+45t-3=0

Solution for -66t^2+45t-3=0 equation:

Simplifying
-66t2 + 45t + -3 = 0

Reorder the terms:
-3 + 45t + -66t2 = 0

Solving
-3 + 45t + -66t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 15t + -22t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + 15t + -22t2)' equal to zero and attempt to solve:

Simplifying
-1 + 15t + -22t2 = 0

Solving
-1 + 15t + -22t2 = 0

Begin completing the square.  Divide all terms by
-22 the coefficient of the squared term: 

Divide each side by '-22'.
0.04545454545 + -0.6818181818t + t2 = 0

Move the constant term to the right:

Add '-0.04545454545' to each side of the equation.
0.04545454545 + -0.6818181818t + -0.04545454545 + t2 = 0 + -0.04545454545

Reorder the terms:
0.04545454545 + -0.04545454545 + -0.6818181818t + t2 = 0 + -0.04545454545

Combine like terms: 0.04545454545 + -0.04545454545 = 0.00000000000
0.00000000000 + -0.6818181818t + t2 = 0 + -0.04545454545
-0.6818181818t + t2 = 0 + -0.04545454545

Combine like terms: 0 + -0.04545454545 = -0.04545454545
-0.6818181818t + t2 = -0.04545454545

The t term is -0.6818181818t.  Take half its coefficient (-0.3409090909).
Square it (0.1162190083) and add it to both sides.

Add '0.1162190083' to each side of the equation.
-0.6818181818t + 0.1162190083 + t2 = -0.04545454545 + 0.1162190083

Reorder the terms:
0.1162190083 + -0.6818181818t + t2 = -0.04545454545 + 0.1162190083

Combine like terms: -0.04545454545 + 0.1162190083 = 0.07076446285
0.1162190083 + -0.6818181818t + t2 = 0.07076446285

Factor a perfect square on the left side:
(t + -0.3409090909)(t + -0.3409090909) = 0.07076446285

Calculate the square root of the right side: 0.266015907

Break this problem into two subproblems by setting 
(t + -0.3409090909) equal to 0.266015907 and -0.266015907.

Subproblem 1
t + -0.3409090909 = 0.266015907

Simplifying
t + -0.3409090909 = 0.266015907

Reorder the terms:
-0.3409090909 + t = 0.266015907

Solving
-0.3409090909 + t = 0.266015907

Solving for variable 't'.

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

Add '0.3409090909' to each side of the equation.
-0.3409090909 + 0.3409090909 + t = 0.266015907 + 0.3409090909

Combine like terms: -0.3409090909 + 0.3409090909 = 0.0000000000
0.0000000000 + t = 0.266015907 + 0.3409090909
t = 0.266015907 + 0.3409090909

Combine like terms: 0.266015907 + 0.3409090909 = 0.6069249979
t = 0.6069249979

Simplifying
t = 0.6069249979

Subproblem 2
t + -0.3409090909 = -0.266015907

Simplifying
t + -0.3409090909 = -0.266015907

Reorder the terms:
-0.3409090909 + t = -0.266015907

Solving
-0.3409090909 + t = -0.266015907

Solving for variable 't'.

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

Add '0.3409090909' to each side of the equation.
-0.3409090909 + 0.3409090909 + t = -0.266015907 + 0.3409090909

Combine like terms: -0.3409090909 + 0.3409090909 = 0.0000000000
0.0000000000 + t = -0.266015907 + 0.3409090909
t = -0.266015907 + 0.3409090909

Combine like terms: -0.266015907 + 0.3409090909 = 0.0748931839
t = 0.0748931839

Simplifying
t = 0.0748931839

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.6069249979, 0.0748931839}
Solution
t = {0.6069249979, 0.0748931839}