0=t(t+2)

Solution for 0=t(t+2) equation:

Simplifying
0 = t(t + 2)

Reorder the terms:
0 = t(2 + t)
0 = (2 * t + t * t)
0 = (2t + t2)

Solving
0 = 2t + t2

Solving for variable 't'.
Remove the zero:
-2t + -1t2 = 2t + t2 + -2t + -1t2

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

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

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

Factor out the Greatest Common Factor (GCF), '-1t'.
-1t(2 + 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 '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

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

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

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

Simplifying
t = -2
Solution
t = {0, -2}