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

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

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

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

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

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

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

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

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

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

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

Solving
-4 + 9t + -2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-4 + t)(1 + -2t) = 0

Subproblem 1
Set the factor '(-4 + t)' equal to zero and attempt to solve:

Simplifying
-4 + t = 0

Solving
-4 + t = 0

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

Add '4' to each side of the equation.
-4 + 4 + t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + t = 0 + 4
t = 0 + 4

Combine like terms: 0 + 4 = 4
t = 4

Simplifying
t = 4
Subproblem 2
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2t = 0 + -1
-2t = 0 + -1

Combine like terms: 0 + -1 = -1
-2t = -1

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Solution
t = {4, 0.5}