4t+t(t+9)=0

Solution for 4t+t(t+9)=0 equation:

Simplifying
4t + t(t + 9) = 0

Reorder the terms:
4t + t(9 + t) = 0
4t + (9 * t + t * t) = 0
4t + (9t + t2) = 0

Combine like terms: 4t + 9t = 13t
13t + t2 = 0

Solving
13t + t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(13 + t) = 0

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 '(13 + t)' equal to zero and attempt to solve:

Simplifying
13 + t = 0

Solving
13 + t = 0

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

Add '-13' to each side of the equation.
13 + -13 + t = 0 + -13

Combine like terms: 13 + -13 = 0
0 + t = 0 + -13
t = 0 + -13

Combine like terms: 0 + -13 = -13
t = -13

Simplifying
t = -13
Solution
t = {0, -13}