(3t^2-4t+1)+(-6t^2+7t+5)=

Solution for (3t^2-4t+1)+(-6t^2+7t+5)= equation:

Simplifying
(3t2 + -4t + 1) + (-6t2 + 7t + 5) = 0

Reorder the terms:
(1 + -4t + 3t2) + (-6t2 + 7t + 5) = 0

Remove parenthesis around (1 + -4t + 3t2)
1 + -4t + 3t2 + (-6t2 + 7t + 5) = 0

Reorder the terms:
1 + -4t + 3t2 + (5 + 7t + -6t2) = 0

Remove parenthesis around (5 + 7t + -6t2)
1 + -4t + 3t2 + 5 + 7t + -6t2 = 0

Reorder the terms:
1 + 5 + -4t + 7t + 3t2 + -6t2 = 0

Combine like terms: 1 + 5 = 6
6 + -4t + 7t + 3t2 + -6t2 = 0

Combine like terms: -4t + 7t = 3t
6 + 3t + 3t2 + -6t2 = 0

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

Solving
6 + 3t + -3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + t + -1t2) = 0

Factor a trinomial.
3((2 + -1t)(1 + t)) = 0

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

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

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

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

Divide each side by '-1'.
t = 2

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

Simplifying
1 + t = 0

Solving
1 + t = 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 + t = 0 + -1

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

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

Simplifying
t = -1
Solution
t = {2, -1}