(t+5)(t-6)=0

Solution for (t+5)(t-6)=0 equation:

Simplifying
(t + 5)(t + -6) = 0

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

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

Multiply (5 + t) * (-6 + t)
(5(-6 + t) + t(-6 + t)) = 0
((-6 * 5 + t * 5) + t(-6 + t)) = 0
((-30 + 5t) + t(-6 + t)) = 0
(-30 + 5t + (-6 * t + t * t)) = 0
(-30 + 5t + (-6t + t2)) = 0

Combine like terms: 5t + -6t = -1t
(-30 + -1t + t2) = 0

Solving
-30 + -1t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-5 + -1t)(6 + -1t) = 0

Subproblem 1
Set the factor '(-5 + -1t)' equal to zero and attempt to solve:

Simplifying
-5 + -1t = 0

Solving
-5 + -1t = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1t = 0 + 5
-1t = 0 + 5

Combine like terms: 0 + 5 = 5
-1t = 5

Divide each side by '-1'.
t = -5

Simplifying
t = -5
Subproblem 2
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
Solution
t = {-5, 6}