(t+3)(t-15)=0

Solution for (t+3)(t-15)=0 equation:

Simplifying
(t + 3)(t + -15) = 0

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

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

Multiply (3 + t) * (-15 + t)
(3(-15 + t) + t(-15 + t)) = 0
((-15 * 3 + t * 3) + t(-15 + t)) = 0
((-45 + 3t) + t(-15 + t)) = 0
(-45 + 3t + (-15 * t + t * t)) = 0
(-45 + 3t + (-15t + t2)) = 0

Combine like terms: 3t + -15t = -12t
(-45 + -12t + t2) = 0

Solving
-45 + -12t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-3 + -1t)(15 + -1t) = 0

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

Simplifying
-3 + -1t = 0

Solving
-3 + -1t = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1t = 0 + 3
-1t = 0 + 3

Combine like terms: 0 + 3 = 3
-1t = 3

Divide each side by '-1'.
t = -3

Simplifying
t = -3
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 = {-3, 15}