(t-6)(t+9)=0

Solution for (t-6)(t+9)=0 equation:

Simplifying
(t + -6)(t + 9) = 0

Reorder the terms:
(-6 + t)(t + 9) = 0

Reorder the terms:
(-6 + t)(9 + t) = 0

Multiply (-6 + t) * (9 + t)
(-6(9 + t) + t(9 + t)) = 0
((9 * -6 + t * -6) + t(9 + t)) = 0
((-54 + -6t) + t(9 + t)) = 0
(-54 + -6t + (9 * t + t * t)) = 0
(-54 + -6t + (9t + t2)) = 0

Combine like terms: -6t + 9t = 3t
(-54 + 3t + t2) = 0

Solving
-54 + 3t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-9 + -1t)(6 + -1t) = 0

Subproblem 1
Set the factor '(-9 + -1t)' equal to zero and attempt to solve:

Simplifying
-9 + -1t = 0

Solving
-9 + -1t = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1t = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1t = 0 + 9
-1t = 0 + 9

Combine like terms: 0 + 9 = 9
-1t = 9

Divide each side by '-1'.
t = -9

Simplifying
t = -9
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 = {-9, 6}