t(t+4)1=t(t+2)+2

Solution for t(t+4)1=t(t+2)+2 equation:

Simplifying
t(t + 4) * 1 = t(t + 2) + 2

Reorder the terms:
t(4 + t) * 1 = t(t + 2) + 2

Reorder the terms for easier multiplication:
1t(4 + t) = t(t + 2) + 2
(4 * 1t + t * 1t) = t(t + 2) + 2
(4t + 1t2) = t(t + 2) + 2

Reorder the terms:
4t + 1t2 = t(2 + t) + 2
4t + 1t2 = (2 * t + t * t) + 2
4t + 1t2 = (2t + t2) + 2

Reorder the terms:
4t + 1t2 = 2 + 2t + t2

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

Solving for variable 't'.

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

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + t) = 0

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

Simplifying
-1 + t = 0

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

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

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

Simplifying
t = 1
Solution
t = {1}