T(t-6)(t+15)=0

Solution for T(t-6)(t+15)=0 equation:

Simplifying
T(t + -6)(t + 15) = 0

Reorder the terms:
T(-6 + t)(t + 15) = 0

Reorder the terms:
T(-6 + t)(15 + t) = 0

Multiply (-6 + t) * (15 + t)
T(-6(15 + t) + t(15 + t)) = 0
T((15 * -6 + t * -6) + t(15 + t)) = 0
T((-90 + -6t) + t(15 + t)) = 0
T(-90 + -6t + (15 * t + t * t)) = 0
T(-90 + -6t + (15t + t2)) = 0

Combine like terms: -6t + 15t = 9t
T(-90 + 9t + t2) = 0
(-90 * T + 9t * T + t2 * T) = 0
(-90T + 9tT + t2T) = 0

Solving
-90T + 9tT + t2T = 0

Solving for variable 'T'.

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

Factor out the Greatest Common Factor (GCF), 'T'.
T(-90 + 9t + t2) = 0

Factor a trinomial.
T((-15 + -1t)(6 + -1t)) = 0

Subproblem 1
Set the factor 'T' equal to zero and attempt to solve:

Simplifying
T = 0

Solving
T = 0

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

Simplifying
T = 0
Subproblem 2
Set the factor '(-15 + -1t)' equal to zero and attempt to solve:

Simplifying
-15 + -1t = 0

Solving
-15 + -1t = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1t = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1t = 0 + 15
-1t = 0 + 15

Combine like terms: 0 + 15 = 15
-1t = 15

Add 't' to each side of the equation.
-1t + t = 15 + t

Combine like terms: -1t + t = 0
0 = 15 + t

Simplifying
0 = 15 + t

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Add 't' to each side of the equation.
-1t + t = -6 + t

Combine like terms: -1t + t = 0
0 = -6 + t

Simplifying
0 = -6 + t

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
T = {0}