(t+3)(t-12)=0

Solution for (t+3)(t-12)=0 equation:

Simplifying
(t + 3)(t + -12) = 0

Reorder the terms:
(3 + t)(t + -12) = 0

Reorder the terms:
(3 + t)(-12 + t) = 0

Multiply (3 + t) * (-12 + t)
(3(-12 + t) + t(-12 + t)) = 0
((-12 * 3 + t * 3) + t(-12 + t)) = 0
((-36 + 3t) + t(-12 + t)) = 0
(-36 + 3t + (-12 * t + t * t)) = 0
(-36 + 3t + (-12t + t2)) = 0

Combine like terms: 3t + -12t = -9t
(-36 + -9t + t2) = 0

Solving
-36 + -9t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-3 + -1t)(12 + -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 '(12 + -1t)' equal to zero and attempt to solve:

Simplifying
12 + -1t = 0

Solving
12 + -1t = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1t = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1t = 0 + -12
-1t = 0 + -12

Combine like terms: 0 + -12 = -12
-1t = -12

Divide each side by '-1'.
t = 12

Simplifying
t = 12
Solution
t = {-3, 12}