61=61-6t-5t^2

Solution for 61=61-6t-5t^2 equation:

Simplifying
61 = 61 + -6t + -5t2

Add '-61' to each side of the equation.
61 + -61 = 61 + -6t + -61 + -5t2

Combine like terms: 61 + -61 = 0
0 = 61 + -6t + -61 + -5t2

Reorder the terms:
0 = 61 + -61 + -6t + -5t2

Combine like terms: 61 + -61 = 0
0 = 0 + -6t + -5t2
0 = -6t + -5t2

Solving
0 = -6t + -5t2

Solving for variable 't'.
Remove the zero:
6t + 5t2 = -6t + -5t2 + 6t + 5t2

Reorder the terms:
6t + 5t2 = -6t + 6t + -5t2 + 5t2

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

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

Factor out the Greatest Common Factor (GCF), 't'.
t(6 + 5t) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(6 + 5t)' equal to zero and attempt to solve:

Simplifying
6 + 5t = 0

Solving
6 + 5t = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5t = 0 + -6
5t = 0 + -6

Combine like terms: 0 + -6 = -6
5t = -6

Divide each side by '5'.
t = -1.2

Simplifying
t = -1.2
Solution
t = {0, -1.2}