2(5-t)t+6t=t+22

Solution for 2(5-t)t+6t=t+22 equation:

Simplifying
2(5 + -1t) * t + 6t = t + 22

Reorder the terms for easier multiplication:
2t(5 + -1t) + 6t = t + 22
(5 * 2t + -1t * 2t) + 6t = t + 22
(10t + -2t2) + 6t = t + 22

Reorder the terms:
10t + 6t + -2t2 = t + 22

Combine like terms: 10t + 6t = 16t
16t + -2t2 = t + 22

Reorder the terms:
16t + -2t2 = 22 + t

Solving
16t + -2t2 = 22 + t

Solving for variable 't'.

Reorder the terms:
-22 + 16t + -1t + -2t2 = 22 + t + -22 + -1t

Combine like terms: 16t + -1t = 15t
-22 + 15t + -2t2 = 22 + t + -22 + -1t

Reorder the terms:
-22 + 15t + -2t2 = 22 + -22 + t + -1t

Combine like terms: 22 + -22 = 0
-22 + 15t + -2t2 = 0 + t + -1t
-22 + 15t + -2t2 = t + -1t

Combine like terms: t + -1t = 0
-22 + 15t + -2t2 = 0

Factor a trinomial.
(-11 + 2t)(2 + -1t) = 0

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

Simplifying
-11 + 2t = 0

Solving
-11 + 2t = 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 + 2t = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 2t = 0 + 11
2t = 0 + 11

Combine like terms: 0 + 11 = 11
2t = 11

Divide each side by '2'.
t = 5.5

Simplifying
t = 5.5
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 = {5.5, 2}