11=1+15t-5t^2

Solution for 11=1+15t-5t^2 equation:

Simplifying
11 = 1 + 15t + -5t2

Solving
11 = 1 + 15t + -5t2

Solving for variable 't'.

Combine like terms: 11 + -1 = 10
10 + -15t + 5t2 = 1 + 15t + -5t2 + -1 + -15t + 5t2

Reorder the terms:
10 + -15t + 5t2 = 1 + -1 + 15t + -15t + -5t2 + 5t2

Combine like terms: 1 + -1 = 0
10 + -15t + 5t2 = 0 + 15t + -15t + -5t2 + 5t2
10 + -15t + 5t2 = 15t + -15t + -5t2 + 5t2

Combine like terms: 15t + -15t = 0
10 + -15t + 5t2 = 0 + -5t2 + 5t2
10 + -15t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
10 + -15t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -3t + t2) = 0

Factor a trinomial.
5((1 + -1t)(2 + -1t)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

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

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

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

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

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