18t^2+78t+72=0

Solution for 18t^2+78t+72=0 equation:

Simplifying
18t2 + 78t + 72 = 0

Reorder the terms:
72 + 78t + 18t2 = 0

Solving
72 + 78t + 18t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + 13t + 3t2) = 0

Factor a trinomial.
6((3 + t)(4 + 3t)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

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

Add '-3' to each side of the equation.
3 + -3 + t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t = 0 + -3
t = 0 + -3

Combine like terms: 0 + -3 = -3
t = -3

Simplifying
t = -3
Subproblem 2
Set the factor '(4 + 3t)' equal to zero and attempt to solve:

Simplifying
4 + 3t = 0

Solving
4 + 3t = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3t = 0 + -4
3t = 0 + -4

Combine like terms: 0 + -4 = -4
3t = -4

Divide each side by '3'.
t = -1.333333333

Simplifying
t = -1.333333333
Solution
t = {-3, -1.333333333}