22=(-2t+9)(t+4)

Solution for 22=(-2t+9)(t+4) equation:

Simplifying
22 = (-2t + 9)(t + 4)

Reorder the terms:
22 = (9 + -2t)(t + 4)

Reorder the terms:
22 = (9 + -2t)(4 + t)

Multiply (9 + -2t) * (4 + t)
22 = (9(4 + t) + -2t * (4 + t))
22 = ((4 * 9 + t * 9) + -2t * (4 + t))
22 = ((36 + 9t) + -2t * (4 + t))
22 = (36 + 9t + (4 * -2t + t * -2t))
22 = (36 + 9t + (-8t + -2t2))

Combine like terms: 9t + -8t = 1t
22 = (36 + 1t + -2t2)

Solving
22 = 36 + 1t + -2t2

Solving for variable 't'.

Combine like terms: 22 + -36 = -14
-14 + -1t + 2t2 = 36 + 1t + -2t2 + -36 + -1t + 2t2

Reorder the terms:
-14 + -1t + 2t2 = 36 + -36 + 1t + -1t + -2t2 + 2t2

Combine like terms: 36 + -36 = 0
-14 + -1t + 2t2 = 0 + 1t + -1t + -2t2 + 2t2
-14 + -1t + 2t2 = 1t + -1t + -2t2 + 2t2

Combine like terms: 1t + -1t = 0
-14 + -1t + 2t2 = 0 + -2t2 + 2t2
-14 + -1t + 2t2 = -2t2 + 2t2

Combine like terms: -2t2 + 2t2 = 0
-14 + -1t + 2t2 = 0

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

Divide each side by '2'.
-7 + -0.5t + t2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -0.5t + 7 + t2 = 0 + 7

Reorder the terms:
-7 + 7 + -0.5t + t2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -0.5t + t2 = 0 + 7
-0.5t + t2 = 0 + 7

Combine like terms: 0 + 7 = 7
-0.5t + t2 = 7

The t term is -0.5t.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5t + 0.0625 + t2 = 7 + 0.0625

Reorder the terms:
0.0625 + -0.5t + t2 = 7 + 0.0625

Combine like terms: 7 + 0.0625 = 7.0625
0.0625 + -0.5t + t2 = 7.0625

Factor a perfect square on the left side:
(t + -0.25)(t + -0.25) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(t + -0.25) equal to 2.657536453 and -2.657536453.

Subproblem 1
t + -0.25 = 2.657536453

Simplifying
t + -0.25 = 2.657536453

Reorder the terms:
-0.25 + t = 2.657536453

Solving
-0.25 + t = 2.657536453

Solving for variable 't'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + t = 2.657536453 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + t = 2.657536453 + 0.25
t = 2.657536453 + 0.25

Combine like terms: 2.657536453 + 0.25 = 2.907536453
t = 2.907536453

Simplifying
t = 2.907536453

Subproblem 2
t + -0.25 = -2.657536453

Simplifying
t + -0.25 = -2.657536453

Reorder the terms:
-0.25 + t = -2.657536453

Solving
-0.25 + t = -2.657536453

Solving for variable 't'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + t = -2.657536453 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + t = -2.657536453 + 0.25
t = -2.657536453 + 0.25

Combine like terms: -2.657536453 + 0.25 = -2.407536453
t = -2.407536453

Simplifying
t = -2.407536453

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.907536453, -2.407536453}