6t^2+30ty+24y^2=0

Solution for 6t^2+30ty+24y^2=0 equation:

Simplifying
6t2 + 30ty + 24y2 = 0

Reorder the terms:
30ty + 6t2 + 24y2 = 0

Solving
30ty + 6t2 + 24y2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(5ty + t2 + 4y2) = 0

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

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

Simplifying
t + y = 0

Solving
t + y = 0

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

Add '-1y' to each side of the equation.
t + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
t + 0 = 0 + -1y
t = 0 + -1y
Remove the zero:
t = -1y

Simplifying
t = -1y
Subproblem 2
Set the factor '(t + 4y)' equal to zero and attempt to solve:

Simplifying
t + 4y = 0

Solving
t + 4y = 0

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

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

Combine like terms: 4y + -4y = 0
t + 0 = 0 + -4y
t = 0 + -4y
Remove the zero:
t = -4y

Simplifying
t = -4y
Solution
t = {-1y, -4y}