3t^4+15t^3+18t^2=

Solution for 3t^4+15t^3+18t^2= equation:

Simplifying
3t4 + 15t3 + 18t2 = 0

Reorder the terms:
18t2 + 15t3 + 3t4 = 0

Solving
18t2 + 15t3 + 3t4 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3t2'.
3t2(6 + 5t + t2) = 0

Factor a trinomial.
3t2((3 + t)(2 + t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 't2' equal to zero and attempt to solve:

Simplifying
t2 = 0

Solving
t2 = 0

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

Simplifying
t2 = 0

Take the square root of each side:
t = {0}
Subproblem 2
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 3
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, -3, -2}