t(11t+1)=10

Solution for t(11t+1)=10 equation:

Simplifying
t(11t + 1) = 10

Reorder the terms:
t(1 + 11t) = 10
(1 * t + 11t * t) = 10
(1t + 11t2) = 10

Solving
1t + 11t2 = 10

Solving for variable 't'.

Reorder the terms:
-10 + 1t + 11t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 1t + 11t2 = 0

Factor a trinomial.
(-1 + -1t)(10 + -11t) = 0

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 '(10 + -11t)' equal to zero and attempt to solve:

Simplifying
10 + -11t = 0

Solving
10 + -11t = 0

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

Add '-10' to each side of the equation.
10 + -10 + -11t = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -11t = 0 + -10
-11t = 0 + -10

Combine like terms: 0 + -10 = -10
-11t = -10

Divide each side by '-11'.
t = 0.9090909091

Simplifying
t = 0.9090909091
Solution
t = {-1, 0.9090909091}