(3t^2-2t)+(9t^2+4t-6)=0

Solution for (3t^2-2t)+(9t^2+4t-6)=0 equation:

Simplifying
(3t2 + -2t) + (9t2 + 4t + -6) = 0

Reorder the terms:
(-2t + 3t2) + (9t2 + 4t + -6) = 0

Remove parenthesis around (-2t + 3t2)
-2t + 3t2 + (9t2 + 4t + -6) = 0

Reorder the terms:
-2t + 3t2 + (-6 + 4t + 9t2) = 0

Remove parenthesis around (-6 + 4t + 9t2)
-2t + 3t2 + -6 + 4t + 9t2 = 0

Reorder the terms:
-6 + -2t + 4t + 3t2 + 9t2 = 0

Combine like terms: -2t + 4t = 2t
-6 + 2t + 3t2 + 9t2 = 0

Combine like terms: 3t2 + 9t2 = 12t2
-6 + 2t + 12t2 = 0

Solving
-6 + 2t + 12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + t + 6t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + t + 6t2)' equal to zero and attempt to solve:

Simplifying
-3 + t + 6t2 = 0

Solving
-3 + t + 6t2 = 0

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

Divide each side by '6'.
-0.5 + 0.1666666667t + t2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.1666666667t + 0.5 + t2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.1666666667t + t2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.1666666667t + t2 = 0 + 0.5
0.1666666667t + t2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.1666666667t + t2 = 0.5

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1666666667t + 0.25 + t2 = 0.5 + 0.25

Reorder the terms:
0.25 + 0.1666666667t + t2 = 0.5 + 0.25

Combine like terms: 0.5 + 0.25 = 0.75
0.25 + 0.1666666667t + t2 = 0.75

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(t + 0.5) equal to 0.866025404 and -0.866025404.

Subproblem 1
t + 0.5 = 0.866025404

Simplifying
t + 0.5 = 0.866025404

Reorder the terms:
0.5 + t = 0.866025404

Solving
0.5 + t = 0.866025404

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 0.866025404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 0.866025404 + -0.5
t = 0.866025404 + -0.5

Combine like terms: 0.866025404 + -0.5 = 0.366025404
t = 0.366025404

Simplifying
t = 0.366025404

Subproblem 2
t + 0.5 = -0.866025404

Simplifying
t + 0.5 = -0.866025404

Reorder the terms:
0.5 + t = -0.866025404

Solving
0.5 + t = -0.866025404

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -0.866025404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -0.866025404 + -0.5
t = -0.866025404 + -0.5

Combine like terms: -0.866025404 + -0.5 = -1.366025404
t = -1.366025404

Simplifying
t = -1.366025404

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.366025404, -1.366025404}
Solution
t = {0.366025404, -1.366025404}