t^2+10ty+21y^2=0

Solution for t^2+10ty+21y^2=0 equation:

Simplifying
t2 + 10ty + 21y2 = 0

Reorder the terms:
10ty + t2 + 21y2 = 0

Solving
10ty + t2 + 21y2 = 0

Solving for variable 't'.

Factor a trinomial.
(t + 3y)(t + 7y) = 0

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

Simplifying
t + 3y = 0

Solving
t + 3y = 0

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

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

Combine like terms: 3y + -3y = 0
t + 0 = 0 + -3y
t = 0 + -3y
Remove the zero:
t = -3y

Simplifying
t = -3y
Subproblem 2
Set the factor '(t + 7y)' equal to zero and attempt to solve:

Simplifying
t + 7y = 0

Solving
t + 7y = 0

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

Add '-7y' to each side of the equation.
t + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
t + 0 = 0 + -7y
t = 0 + -7y
Remove the zero:
t = -7y

Simplifying
t = -7y
Solution
t = {-3y, -7y}