2t(t+3)+4=0

Solution for 2t(t+3)+4=0 equation:

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

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

Reorder the terms:
4 + 6t + 2t2 = 0

Solving
4 + 6t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 3t + t2) = 0

Factor a trinomial.
2((2 + t)(1 + t)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {-2, -1}