(3t^2-5t-6)+(2t^2-4t+1)=0

Solution for (3t^2-5t-6)+(2t^2-4t+1)=0 equation:

Simplifying
(3t2 + -5t + -6) + (2t2 + -4t + 1) = 0

Reorder the terms:
(-6 + -5t + 3t2) + (2t2 + -4t + 1) = 0

Remove parenthesis around (-6 + -5t + 3t2)
-6 + -5t + 3t2 + (2t2 + -4t + 1) = 0

Reorder the terms:
-6 + -5t + 3t2 + (1 + -4t + 2t2) = 0

Remove parenthesis around (1 + -4t + 2t2)
-6 + -5t + 3t2 + 1 + -4t + 2t2 = 0

Reorder the terms:
-6 + 1 + -5t + -4t + 3t2 + 2t2 = 0

Combine like terms: -6 + 1 = -5
-5 + -5t + -4t + 3t2 + 2t2 = 0

Combine like terms: -5t + -4t = -9t
-5 + -9t + 3t2 + 2t2 = 0

Combine like terms: 3t2 + 2t2 = 5t2
-5 + -9t + 5t2 = 0

Solving
-5 + -9t + 5t2 = 0

Solving for variable 't'.

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

Divide each side by '5'.
-1 + -1.8t + t2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.8t + 1 + t2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.8t + t2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.8t + t2 = 0 + 1
-1.8t + t2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.8t + t2 = 1

The t term is -1.8t.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8t + 0.81 + t2 = 1 + 0.81

Reorder the terms:
0.81 + -1.8t + t2 = 1 + 0.81

Combine like terms: 1 + 0.81 = 1.81
0.81 + -1.8t + t2 = 1.81

Factor a perfect square on the left side:
(t + -0.9)(t + -0.9) = 1.81

Calculate the square root of the right side: 1.345362405

Break this problem into two subproblems by setting 
(t + -0.9) equal to 1.345362405 and -1.345362405.

Subproblem 1
t + -0.9 = 1.345362405

Simplifying
t + -0.9 = 1.345362405

Reorder the terms:
-0.9 + t = 1.345362405

Solving
-0.9 + t = 1.345362405

Solving for variable 't'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + t = 1.345362405 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + t = 1.345362405 + 0.9
t = 1.345362405 + 0.9

Combine like terms: 1.345362405 + 0.9 = 2.245362405
t = 2.245362405

Simplifying
t = 2.245362405

Subproblem 2
t + -0.9 = -1.345362405

Simplifying
t + -0.9 = -1.345362405

Reorder the terms:
-0.9 + t = -1.345362405

Solving
-0.9 + t = -1.345362405

Solving for variable 't'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + t = -1.345362405 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + t = -1.345362405 + 0.9
t = -1.345362405 + 0.9

Combine like terms: -1.345362405 + 0.9 = -0.445362405
t = -0.445362405

Simplifying
t = -0.445362405

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.245362405, -0.445362405}