72=(t-8)(t+9)

Solution for 72=(t-8)(t+9) equation:

Simplifying
72 = (t + -8)(t + 9)

Reorder the terms:
72 = (-8 + t)(t + 9)

Reorder the terms:
72 = (-8 + t)(9 + t)

Multiply (-8 + t) * (9 + t)
72 = (-8(9 + t) + t(9 + t))
72 = ((9 * -8 + t * -8) + t(9 + t))
72 = ((-72 + -8t) + t(9 + t))
72 = (-72 + -8t + (9 * t + t * t))
72 = (-72 + -8t + (9t + t2))

Combine like terms: -8t + 9t = 1t
72 = (-72 + 1t + t2)

Solving
72 = -72 + 1t + t2

Solving for variable 't'.

Combine like terms: 72 + 72 = 144
144 + -1t + -1t2 = -72 + 1t + t2 + 72 + -1t + -1t2

Reorder the terms:
144 + -1t + -1t2 = -72 + 72 + 1t + -1t + t2 + -1t2

Combine like terms: -72 + 72 = 0
144 + -1t + -1t2 = 0 + 1t + -1t + t2 + -1t2
144 + -1t + -1t2 = 1t + -1t + t2 + -1t2

Combine like terms: 1t + -1t = 0
144 + -1t + -1t2 = 0 + t2 + -1t2
144 + -1t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
144 + -1t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-144 + t + t2 = 0

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + t + 144 + t2 = 0 + 144

Reorder the terms:
-144 + 144 + t + t2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + t + t2 = 0 + 144
t + t2 = 0 + 144

Combine like terms: 0 + 144 = 144
t + t2 = 144

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + t2 = 144 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + t2 = 144 + 0.25

Combine like terms: 144 + 0.25 = 144.25
1.25 + t2 = 144.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 144.25

Calculate the square root of the right side: 12.010412149

Break this problem into two subproblems by setting 
(t + 0.5) equal to 12.010412149 and -12.010412149.

Subproblem 1
t + 0.5 = 12.010412149

Simplifying
t + 0.5 = 12.010412149

Reorder the terms:
0.5 + t = 12.010412149

Solving
0.5 + t = 12.010412149

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 12.010412149 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 12.010412149 + -0.5
t = 12.010412149 + -0.5

Combine like terms: 12.010412149 + -0.5 = 11.510412149
t = 11.510412149

Simplifying
t = 11.510412149

Subproblem 2
t + 0.5 = -12.010412149

Simplifying
t + 0.5 = -12.010412149

Reorder the terms:
0.5 + t = -12.010412149

Solving
0.5 + t = -12.010412149

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -12.010412149 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -12.010412149 + -0.5
t = -12.010412149 + -0.5

Combine like terms: -12.010412149 + -0.5 = -12.510412149
t = -12.510412149

Simplifying
t = -12.510412149

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.510412149, -12.510412149}