t(9t-10)=(6t-4)

Solution for t(9t-10)=(6t-4) equation:

Simplifying
t(9t + -10) = (6t + -4)

Reorder the terms:
t(-10 + 9t) = (6t + -4)
(-10 * t + 9t * t) = (6t + -4)
(-10t + 9t2) = (6t + -4)

Reorder the terms:
-10t + 9t2 = (-4 + 6t)

Remove parenthesis around (-4 + 6t)
-10t + 9t2 = -4 + 6t

Solving
-10t + 9t2 = -4 + 6t

Solving for variable 't'.

Reorder the terms:
4 + -10t + -6t + 9t2 = -4 + 6t + 4 + -6t

Combine like terms: -10t + -6t = -16t
4 + -16t + 9t2 = -4 + 6t + 4 + -6t

Reorder the terms:
4 + -16t + 9t2 = -4 + 4 + 6t + -6t

Combine like terms: -4 + 4 = 0
4 + -16t + 9t2 = 0 + 6t + -6t
4 + -16t + 9t2 = 6t + -6t

Combine like terms: 6t + -6t = 0
4 + -16t + 9t2 = 0

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

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

Move the constant term to the right:

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

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

Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000
0.0000000000 + -1.777777778t + t2 = 0 + -0.4444444444
-1.777777778t + t2 = 0 + -0.4444444444

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

The t term is -1.777777778t.  Take half its coefficient (-0.888888889).
Square it (0.7901234570) and add it to both sides.

Add '0.7901234570' to each side of the equation.
-1.777777778t + 0.7901234570 + t2 = -0.4444444444 + 0.7901234570

Reorder the terms:
0.7901234570 + -1.777777778t + t2 = -0.4444444444 + 0.7901234570

Combine like terms: -0.4444444444 + 0.7901234570 = 0.3456790126
0.7901234570 + -1.777777778t + t2 = 0.3456790126

Factor a perfect square on the left side:
(t + -0.888888889)(t + -0.888888889) = 0.3456790126

Calculate the square root of the right side: 0.587944736

Break this problem into two subproblems by setting 
(t + -0.888888889) equal to 0.587944736 and -0.587944736.

Subproblem 1
t + -0.888888889 = 0.587944736

Simplifying
t + -0.888888889 = 0.587944736

Reorder the terms:
-0.888888889 + t = 0.587944736

Solving
-0.888888889 + t = 0.587944736

Solving for variable 't'.

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

Add '0.888888889' to each side of the equation.
-0.888888889 + 0.888888889 + t = 0.587944736 + 0.888888889

Combine like terms: -0.888888889 + 0.888888889 = 0.000000000
0.000000000 + t = 0.587944736 + 0.888888889
t = 0.587944736 + 0.888888889

Combine like terms: 0.587944736 + 0.888888889 = 1.476833625
t = 1.476833625

Simplifying
t = 1.476833625

Subproblem 2
t + -0.888888889 = -0.587944736

Simplifying
t + -0.888888889 = -0.587944736

Reorder the terms:
-0.888888889 + t = -0.587944736

Solving
-0.888888889 + t = -0.587944736

Solving for variable 't'.

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

Add '0.888888889' to each side of the equation.
-0.888888889 + 0.888888889 + t = -0.587944736 + 0.888888889

Combine like terms: -0.888888889 + 0.888888889 = 0.000000000
0.000000000 + t = -0.587944736 + 0.888888889
t = -0.587944736 + 0.888888889

Combine like terms: -0.587944736 + 0.888888889 = 0.300944153
t = 0.300944153

Simplifying
t = 0.300944153

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.476833625, 0.300944153}