(-12)t=(t-8)(t+8)

Solution for (-12)t=(t-8)(t+8) equation:

Simplifying
(-12) * t = (t + -8)(t + 8)

Reorder the terms:
-12t = (-8 + t)(t + 8)

Reorder the terms:
-12t = (-8 + t)(8 + t)

Multiply (-8 + t) * (8 + t)
-12t = (-8(8 + t) + t(8 + t))
-12t = ((8 * -8 + t * -8) + t(8 + t))
-12t = ((-64 + -8t) + t(8 + t))
-12t = (-64 + -8t + (8 * t + t * t))
-12t = (-64 + -8t + (8t + t2))

Combine like terms: -8t + 8t = 0
-12t = (-64 + 0 + t2)
-12t = (-64 + t2)

Solving
-12t = -64 + t2

Solving for variable 't'.

Reorder the terms:
64 + -12t + -1t2 = -64 + t2 + 64 + -1t2

Reorder the terms:
64 + -12t + -1t2 = -64 + 64 + t2 + -1t2

Combine like terms: -64 + 64 = 0
64 + -12t + -1t2 = 0 + t2 + -1t2
64 + -12t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
64 + -12t + -1t2 = 0

Factor a trinomial.
(4 + -1t)(16 + t) = 0

Subproblem 1
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Subproblem 2
Set the factor '(16 + t)' equal to zero and attempt to solve:

Simplifying
16 + t = 0

Solving
16 + t = 0

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

Add '-16' to each side of the equation.
16 + -16 + t = 0 + -16

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

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

Simplifying
t = -16
Solution
t = {4, -16}