(t)=t^2+2t

Solution for (t)=t^2+2t equation:

Simplifying
(t) = t2 + 2t
t = t2 + 2t

Reorder the terms:
t = 2t + t2

Solving
t = 2t + t2

Solving for variable 't'.

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

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

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

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

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

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

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
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 = {0, -1}