t(3t+4)+3t(3+2t)=

Solution for t(3t+4)+3t(3+2t)= equation:

Simplifying
t(3t + 4) + 3t(3 + 2t) = 0

Reorder the terms:
t(4 + 3t) + 3t(3 + 2t) = 0
(4 * t + 3t * t) + 3t(3 + 2t) = 0
(4t + 3t2) + 3t(3 + 2t) = 0
4t + 3t2 + (3 * 3t + 2t * 3t) = 0
4t + 3t2 + (9t + 6t2) = 0

Reorder the terms:
4t + 9t + 3t2 + 6t2 = 0

Combine like terms: 4t + 9t = 13t
13t + 3t2 + 6t2 = 0

Combine like terms: 3t2 + 6t2 = 9t2
13t + 9t2 = 0

Solving
13t + 9t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(13 + 9t) = 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 + 9t)' equal to zero and attempt to solve:

Simplifying
13 + 9t = 0

Solving
13 + 9t = 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 + 9t = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 9t = 0 + -13
9t = 0 + -13

Combine like terms: 0 + -13 = -13
9t = -13

Divide each side by '9'.
t = -1.444444444

Simplifying
t = -1.444444444
Solution
t = {0, -1.444444444}