1296t=-16(t-9)(t+9)

Solution for 1296t=-16(t-9)(t+9) equation:

Simplifying
1296t = -16(t + -9)(t + 9)

Reorder the terms:
1296t = -16(-9 + t)(t + 9)

Reorder the terms:
1296t = -16(-9 + t)(9 + t)

Multiply (-9 + t) * (9 + t)
1296t = -16(-9(9 + t) + t(9 + t))
1296t = -16((9 * -9 + t * -9) + t(9 + t))
1296t = -16((-81 + -9t) + t(9 + t))
1296t = -16(-81 + -9t + (9 * t + t * t))
1296t = -16(-81 + -9t + (9t + t2))

Combine like terms: -9t + 9t = 0
1296t = -16(-81 + 0 + t2)
1296t = -16(-81 + t2)
1296t = (-81 * -16 + t2 * -16)
1296t = (1296 + -16t2)

Solving
1296t = 1296 + -16t2

Solving for variable 't'.

Reorder the terms:
-1296 + 1296t + 16t2 = 1296 + -16t2 + -1296 + 16t2

Reorder the terms:
-1296 + 1296t + 16t2 = 1296 + -1296 + -16t2 + 16t2

Combine like terms: 1296 + -1296 = 0
-1296 + 1296t + 16t2 = 0 + -16t2 + 16t2
-1296 + 1296t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-1296 + 1296t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-81 + 81t + t2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-81 + 81t + t2)' equal to zero and attempt to solve:

Simplifying
-81 + 81t + t2 = 0

Solving
-81 + 81t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + 81t + 81 + t2 = 0 + 81

Reorder the terms:
-81 + 81 + 81t + t2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 81t + t2 = 0 + 81
81t + t2 = 0 + 81

Combine like terms: 0 + 81 = 81
81t + t2 = 81

The t term is 81t.  Take half its coefficient (40.5).
Square it (1640.25) and add it to both sides.

Add '1640.25' to each side of the equation.
81t + 1640.25 + t2 = 81 + 1640.25

Reorder the terms:
1640.25 + 81t + t2 = 81 + 1640.25

Combine like terms: 81 + 1640.25 = 1721.25
1640.25 + 81t + t2 = 1721.25

Factor a perfect square on the left side:
(t + 40.5)(t + 40.5) = 1721.25

Calculate the square root of the right side: 41.487950058

Break this problem into two subproblems by setting 
(t + 40.5) equal to 41.487950058 and -41.487950058.

Subproblem 1
t + 40.5 = 41.487950058

Simplifying
t + 40.5 = 41.487950058

Reorder the terms:
40.5 + t = 41.487950058

Solving
40.5 + t = 41.487950058

Solving for variable 't'.

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

Add '-40.5' to each side of the equation.
40.5 + -40.5 + t = 41.487950058 + -40.5

Combine like terms: 40.5 + -40.5 = 0.0
0.0 + t = 41.487950058 + -40.5
t = 41.487950058 + -40.5

Combine like terms: 41.487950058 + -40.5 = 0.987950058
t = 0.987950058

Simplifying
t = 0.987950058

Subproblem 2
t + 40.5 = -41.487950058

Simplifying
t + 40.5 = -41.487950058

Reorder the terms:
40.5 + t = -41.487950058

Solving
40.5 + t = -41.487950058

Solving for variable 't'.

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

Add '-40.5' to each side of the equation.
40.5 + -40.5 + t = -41.487950058 + -40.5

Combine like terms: 40.5 + -40.5 = 0.0
0.0 + t = -41.487950058 + -40.5
t = -41.487950058 + -40.5

Combine like terms: -41.487950058 + -40.5 = -81.987950058
t = -81.987950058

Simplifying
t = -81.987950058

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.987950058, -81.987950058}
Solution
t = {0.987950058, -81.987950058}