t(11t+55)=726

Solution for t(11t+55)=726 equation:

Simplifying
t(11t + 55) = 726

Reorder the terms:
t(55 + 11t) = 726
(55 * t + 11t * t) = 726
(55t + 11t2) = 726

Solving
55t + 11t2 = 726

Solving for variable 't'.

Reorder the terms:
-726 + 55t + 11t2 = 726 + -726

Combine like terms: 726 + -726 = 0
-726 + 55t + 11t2 = 0

Factor out the Greatest Common Factor (GCF), '11'.
11(-66 + 5t + t2) = 0

Factor a trinomial.
11((-11 + -1t)(6 + -1t)) = 0

Ignore the factor 11.
Subproblem 1
Set the factor '(-11 + -1t)' equal to zero and attempt to solve:

Simplifying
-11 + -1t = 0

Solving
-11 + -1t = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1t = 0 + 11

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

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

Divide each side by '-1'.
t = -11

Simplifying
t = -11
Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 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 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {-11, 6}