t^2+10ty+24y^2=

Solution for t^2+10ty+24y^2= equation:

Simplifying
t2 + 10ty + 24y2 = 0

Reorder the terms:
10ty + t2 + 24y2 = 0

Solving
10ty + t2 + 24y2 = 0

Solving for variable 't'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(t + 6y)' equal to zero and attempt to solve:

Simplifying
t + 6y = 0

Solving
t + 6y = 0

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

Add '-6y' to each side of the equation.
t + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0
t + 0 = 0 + -6y
t = 0 + -6y
Remove the zero:
t = -6y

Simplifying
t = -6y
Solution
t = {-4y, -6y}