T(2t+1)=(t+2)(t+2)

Solution for T(2t+1)=(t+2)(t+2) equation:

Simplifying
T(2t + 1) = (t + 2)(t + 2)

Reorder the terms:
T(1 + 2t) = (t + 2)(t + 2)
(1 * T + 2t * T) = (t + 2)(t + 2)
(1T + 2tT) = (t + 2)(t + 2)

Reorder the terms:
1T + 2tT = (2 + t)(t + 2)

Reorder the terms:
1T + 2tT = (2 + t)(2 + t)

Multiply (2 + t) * (2 + t)
1T + 2tT = (2(2 + t) + t(2 + t))
1T + 2tT = ((2 * 2 + t * 2) + t(2 + t))
1T + 2tT = ((4 + 2t) + t(2 + t))
1T + 2tT = (4 + 2t + (2 * t + t * t))
1T + 2tT = (4 + 2t + (2t + t2))

Combine like terms: 2t + 2t = 4t
1T + 2tT = (4 + 4t + t2)

Solving
1T + 2tT = 4 + 4t + t2

Solving for variable 'T'.

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

Reorder the terms:
-4 + 1T + -4t + 2tT + -1t2 = 4 + 4t + t2 + -4 + -4t + -1t2

Reorder the terms:
-4 + 1T + -4t + 2tT + -1t2 = 4 + -4 + 4t + -4t + t2 + -1t2

Combine like terms: 4 + -4 = 0
-4 + 1T + -4t + 2tT + -1t2 = 0 + 4t + -4t + t2 + -1t2
-4 + 1T + -4t + 2tT + -1t2 = 4t + -4t + t2 + -1t2

Combine like terms: 4t + -4t = 0
-4 + 1T + -4t + 2tT + -1t2 = 0 + t2 + -1t2
-4 + 1T + -4t + 2tT + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-4 + 1T + -4t + 2tT + -1t2 = 0

The solution to this equation could not be determined.