(t+6)(t-6)=-16t

Solution for (t+6)(t-6)=-16t equation:

Simplifying
(t + 6)(t + -6) = -16t

Reorder the terms:
(6 + t)(t + -6) = -16t

Reorder the terms:
(6 + t)(-6 + t) = -16t

Multiply (6 + t) * (-6 + t)
(6(-6 + t) + t(-6 + t)) = -16t
((-6 * 6 + t * 6) + t(-6 + t)) = -16t
((-36 + 6t) + t(-6 + t)) = -16t
(-36 + 6t + (-6 * t + t * t)) = -16t
(-36 + 6t + (-6t + t2)) = -16t

Combine like terms: 6t + -6t = 0
(-36 + 0 + t2) = -16t
(-36 + t2) = -16t

Solving
-36 + t2 = -16t

Solving for variable 't'.

Reorder the terms:
-36 + 16t + t2 = -16t + 16t

Combine like terms: -16t + 16t = 0
-36 + 16t + t2 = 0

Factor a trinomial.
(-18 + -1t)(2 + -1t) = 0

Subproblem 1
Set the factor '(-18 + -1t)' equal to zero and attempt to solve:

Simplifying
-18 + -1t = 0

Solving
-18 + -1t = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1t = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1t = 0 + 18
-1t = 0 + 18

Combine like terms: 0 + 18 = 18
-1t = 18

Divide each side by '-1'.
t = -18

Simplifying
t = -18
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-18, 2}