6=(t-9)(t+11)

Solution for 6=(t-9)(t+11) equation:

Simplifying
6 = (t + -9)(t + 11)

Reorder the terms:
6 = (-9 + t)(t + 11)

Reorder the terms:
6 = (-9 + t)(11 + t)

Multiply (-9 + t) * (11 + t)
6 = (-9(11 + t) + t(11 + t))
6 = ((11 * -9 + t * -9) + t(11 + t))
6 = ((-99 + -9t) + t(11 + t))
6 = (-99 + -9t + (11 * t + t * t))
6 = (-99 + -9t + (11t + t2))

Combine like terms: -9t + 11t = 2t
6 = (-99 + 2t + t2)

Solving
6 = -99 + 2t + t2

Solving for variable 't'.

Combine like terms: 6 + 99 = 105
105 + -2t + -1t2 = -99 + 2t + t2 + 99 + -2t + -1t2

Reorder the terms:
105 + -2t + -1t2 = -99 + 99 + 2t + -2t + t2 + -1t2

Combine like terms: -99 + 99 = 0
105 + -2t + -1t2 = 0 + 2t + -2t + t2 + -1t2
105 + -2t + -1t2 = 2t + -2t + t2 + -1t2

Combine like terms: 2t + -2t = 0
105 + -2t + -1t2 = 0 + t2 + -1t2
105 + -2t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
105 + -2t + -1t2 = 0

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

Divide each side by '-1'.
-105 + 2t + t2 = 0

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + 2t + 105 + t2 = 0 + 105

Reorder the terms:
-105 + 105 + 2t + t2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 2t + t2 = 0 + 105
2t + t2 = 0 + 105

Combine like terms: 0 + 105 = 105
2t + t2 = 105

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 105 + 1

Reorder the terms:
1 + 2t + t2 = 105 + 1

Combine like terms: 105 + 1 = 106
1 + 2t + t2 = 106

Factor a perfect square on the left side:
(t + 1)(t + 1) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(t + 1) equal to 10.295630141 and -10.295630141.

Subproblem 1
t + 1 = 10.295630141

Simplifying
t + 1 = 10.295630141

Reorder the terms:
1 + t = 10.295630141

Solving
1 + t = 10.295630141

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 10.295630141 + -1

Combine like terms: 1 + -1 = 0
0 + t = 10.295630141 + -1
t = 10.295630141 + -1

Combine like terms: 10.295630141 + -1 = 9.295630141
t = 9.295630141

Simplifying
t = 9.295630141

Subproblem 2
t + 1 = -10.295630141

Simplifying
t + 1 = -10.295630141

Reorder the terms:
1 + t = -10.295630141

Solving
1 + t = -10.295630141

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -10.295630141 + -1

Combine like terms: 1 + -1 = 0
0 + t = -10.295630141 + -1
t = -10.295630141 + -1

Combine like terms: -10.295630141 + -1 = -11.295630141
t = -11.295630141

Simplifying
t = -11.295630141

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.295630141, -11.295630141}