9t(3t-5)-6(4-6t)=

Solution for 9t(3t-5)-6(4-6t)= equation:

Simplifying
9t(3t + -5) + -6(4 + -6t) = 0

Reorder the terms:
9t(-5 + 3t) + -6(4 + -6t) = 0
(-5 * 9t + 3t * 9t) + -6(4 + -6t) = 0
(-45t + 27t2) + -6(4 + -6t) = 0
-45t + 27t2 + (4 * -6 + -6t * -6) = 0
-45t + 27t2 + (-24 + 36t) = 0

Reorder the terms:
-24 + -45t + 36t + 27t2 = 0

Combine like terms: -45t + 36t = -9t
-24 + -9t + 27t2 = 0

Solving
-24 + -9t + 27t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -3t + 9t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-8 + -3t + 9t2)' equal to zero and attempt to solve:

Simplifying
-8 + -3t + 9t2 = 0

Solving
-8 + -3t + 9t2 = 0

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

Divide each side by '9'.
-0.8888888889 + -0.3333333333t + t2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + -0.3333333333t + 0.8888888889 + t2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + -0.3333333333t + t2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + -0.3333333333t + t2 = 0 + 0.8888888889
-0.3333333333t + t2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
-0.3333333333t + t2 = 0.8888888889

The t term is -0.3333333333t.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333t + 0.02777777779 + t2 = 0.8888888889 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333t + t2 = 0.8888888889 + 0.02777777779

Combine like terms: 0.8888888889 + 0.02777777779 = 0.91666666669
0.02777777779 + -0.3333333333t + t2 = 0.91666666669

Factor a perfect square on the left side:
(t + -0.1666666667)(t + -0.1666666667) = 0.91666666669

Calculate the square root of the right side: 0.957427108

Break this problem into two subproblems by setting 
(t + -0.1666666667) equal to 0.957427108 and -0.957427108.

Subproblem 1
t + -0.1666666667 = 0.957427108

Simplifying
t + -0.1666666667 = 0.957427108

Reorder the terms:
-0.1666666667 + t = 0.957427108

Solving
-0.1666666667 + t = 0.957427108

Solving for variable 't'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + t = 0.957427108 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + t = 0.957427108 + 0.1666666667
t = 0.957427108 + 0.1666666667

Combine like terms: 0.957427108 + 0.1666666667 = 1.1240937747
t = 1.1240937747

Simplifying
t = 1.1240937747

Subproblem 2
t + -0.1666666667 = -0.957427108

Simplifying
t + -0.1666666667 = -0.957427108

Reorder the terms:
-0.1666666667 + t = -0.957427108

Solving
-0.1666666667 + t = -0.957427108

Solving for variable 't'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + t = -0.957427108 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + t = -0.957427108 + 0.1666666667
t = -0.957427108 + 0.1666666667

Combine like terms: -0.957427108 + 0.1666666667 = -0.7907604413
t = -0.7907604413

Simplifying
t = -0.7907604413

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.1240937747, -0.7907604413}
Solution
t = {1.1240937747, -0.7907604413}