t(9t-2)=2(t+8)

Solution for t(9t-2)=2(t+8) equation:

Simplifying
t(9t + -2) = 2(t + 8)

Reorder the terms:
t(-2 + 9t) = 2(t + 8)
(-2 * t + 9t * t) = 2(t + 8)
(-2t + 9t2) = 2(t + 8)

Reorder the terms:
-2t + 9t2 = 2(8 + t)
-2t + 9t2 = (8 * 2 + t * 2)
-2t + 9t2 = (16 + 2t)

Solving
-2t + 9t2 = 16 + 2t

Solving for variable 't'.

Reorder the terms:
-16 + -2t + -2t + 9t2 = 16 + 2t + -16 + -2t

Combine like terms: -2t + -2t = -4t
-16 + -4t + 9t2 = 16 + 2t + -16 + -2t

Reorder the terms:
-16 + -4t + 9t2 = 16 + -16 + 2t + -2t

Combine like terms: 16 + -16 = 0
-16 + -4t + 9t2 = 0 + 2t + -2t
-16 + -4t + 9t2 = 2t + -2t

Combine like terms: 2t + -2t = 0
-16 + -4t + 9t2 = 0

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

Divide each side by '9'.
-1.777777778 + -0.4444444444t + t2 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + -0.4444444444t + 1.777777778 + t2 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + -0.4444444444t + t2 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + -0.4444444444t + t2 = 0 + 1.777777778
-0.4444444444t + t2 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
-0.4444444444t + t2 = 1.777777778

The t term is -0.4444444444t.  Take half its coefficient (-0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
-0.4444444444t + 0.04938271604 + t2 = 1.777777778 + 0.04938271604

Reorder the terms:
0.04938271604 + -0.4444444444t + t2 = 1.777777778 + 0.04938271604

Combine like terms: 1.777777778 + 0.04938271604 = 1.82716049404
0.04938271604 + -0.4444444444t + t2 = 1.82716049404

Factor a perfect square on the left side:
(t + -0.2222222222)(t + -0.2222222222) = 1.82716049404

Calculate the square root of the right side: 1.351725007

Break this problem into two subproblems by setting 
(t + -0.2222222222) equal to 1.351725007 and -1.351725007.

Subproblem 1
t + -0.2222222222 = 1.351725007

Simplifying
t + -0.2222222222 = 1.351725007

Reorder the terms:
-0.2222222222 + t = 1.351725007

Solving
-0.2222222222 + t = 1.351725007

Solving for variable 't'.

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

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.2222222222 + t = 1.351725007 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + t = 1.351725007 + 0.2222222222
t = 1.351725007 + 0.2222222222

Combine like terms: 1.351725007 + 0.2222222222 = 1.5739472292
t = 1.5739472292

Simplifying
t = 1.5739472292

Subproblem 2
t + -0.2222222222 = -1.351725007

Simplifying
t + -0.2222222222 = -1.351725007

Reorder the terms:
-0.2222222222 + t = -1.351725007

Solving
-0.2222222222 + t = -1.351725007

Solving for variable 't'.

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

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.2222222222 + t = -1.351725007 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + t = -1.351725007 + 0.2222222222
t = -1.351725007 + 0.2222222222

Combine like terms: -1.351725007 + 0.2222222222 = -1.1295027848
t = -1.1295027848

Simplifying
t = -1.1295027848

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.5739472292, -1.1295027848}