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

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

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

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

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

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

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

Solving
-90 + -9t + t2 = 0

Solving for variable 't'.

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

Subproblem 1
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

Divide each side by '-1'.
t = -6

Simplifying
t = -6
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

Divide each side by '-1'.
t = 15

Simplifying
t = 15
Solution
t = {-6, 15}