t(9t-10)=(3t-2)

Solution for t(9t-10)=(3t-2) equation:

Simplifying
t(9t + -10) = (3t + -2)

Reorder the terms:
t(-10 + 9t) = (3t + -2)
(-10 * t + 9t * t) = (3t + -2)
(-10t + 9t2) = (3t + -2)

Reorder the terms:
-10t + 9t2 = (-2 + 3t)

Remove parenthesis around (-2 + 3t)
-10t + 9t2 = -2 + 3t

Solving
-10t + 9t2 = -2 + 3t

Solving for variable 't'.

Reorder the terms:
2 + -10t + -3t + 9t2 = -2 + 3t + 2 + -3t

Combine like terms: -10t + -3t = -13t
2 + -13t + 9t2 = -2 + 3t + 2 + -3t

Reorder the terms:
2 + -13t + 9t2 = -2 + 2 + 3t + -3t

Combine like terms: -2 + 2 = 0
2 + -13t + 9t2 = 0 + 3t + -3t
2 + -13t + 9t2 = 3t + -3t

Combine like terms: 3t + -3t = 0
2 + -13t + 9t2 = 0

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

Divide each side by '9'.
0.2222222222 + -1.444444444t + t2 = 0

Move the constant term to the right:

Add '-0.2222222222' to each side of the equation.
0.2222222222 + -1.444444444t + -0.2222222222 + t2 = 0 + -0.2222222222

Reorder the terms:
0.2222222222 + -0.2222222222 + -1.444444444t + t2 = 0 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + -1.444444444t + t2 = 0 + -0.2222222222
-1.444444444t + t2 = 0 + -0.2222222222

Combine like terms: 0 + -0.2222222222 = -0.2222222222
-1.444444444t + t2 = -0.2222222222

The t term is -1.444444444t.  Take half its coefficient (-0.722222222).
Square it (0.5216049380) and add it to both sides.

Add '0.5216049380' to each side of the equation.
-1.444444444t + 0.5216049380 + t2 = -0.2222222222 + 0.5216049380

Reorder the terms:
0.5216049380 + -1.444444444t + t2 = -0.2222222222 + 0.5216049380

Combine like terms: -0.2222222222 + 0.5216049380 = 0.2993827158
0.5216049380 + -1.444444444t + t2 = 0.2993827158

Factor a perfect square on the left side:
(t + -0.722222222)(t + -0.722222222) = 0.2993827158

Calculate the square root of the right side: 0.547158767

Break this problem into two subproblems by setting 
(t + -0.722222222) equal to 0.547158767 and -0.547158767.

Subproblem 1
t + -0.722222222 = 0.547158767

Simplifying
t + -0.722222222 = 0.547158767

Reorder the terms:
-0.722222222 + t = 0.547158767

Solving
-0.722222222 + t = 0.547158767

Solving for variable 't'.

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

Add '0.722222222' to each side of the equation.
-0.722222222 + 0.722222222 + t = 0.547158767 + 0.722222222

Combine like terms: -0.722222222 + 0.722222222 = 0.000000000
0.000000000 + t = 0.547158767 + 0.722222222
t = 0.547158767 + 0.722222222

Combine like terms: 0.547158767 + 0.722222222 = 1.269380989
t = 1.269380989

Simplifying
t = 1.269380989

Subproblem 2
t + -0.722222222 = -0.547158767

Simplifying
t + -0.722222222 = -0.547158767

Reorder the terms:
-0.722222222 + t = -0.547158767

Solving
-0.722222222 + t = -0.547158767

Solving for variable 't'.

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

Add '0.722222222' to each side of the equation.
-0.722222222 + 0.722222222 + t = -0.547158767 + 0.722222222

Combine like terms: -0.722222222 + 0.722222222 = 0.000000000
0.000000000 + t = -0.547158767 + 0.722222222
t = -0.547158767 + 0.722222222

Combine like terms: -0.547158767 + 0.722222222 = 0.175063455
t = 0.175063455

Simplifying
t = 0.175063455

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.269380989, 0.175063455}