(7t-2)-(-3t+1)=-3t(1-3t)

Solution for (7t-2)-(-3t+1)=-3t(1-3t) equation:

Simplifying
(7t + -2) + -1(-3t + 1) = -3t(1 + -3t)

Reorder the terms:
(-2 + 7t) + -1(-3t + 1) = -3t(1 + -3t)

Remove parenthesis around (-2 + 7t)
-2 + 7t + -1(-3t + 1) = -3t(1 + -3t)

Reorder the terms:
-2 + 7t + -1(1 + -3t) = -3t(1 + -3t)
-2 + 7t + (1 * -1 + -3t * -1) = -3t(1 + -3t)
-2 + 7t + (-1 + 3t) = -3t(1 + -3t)

Reorder the terms:
-2 + -1 + 7t + 3t = -3t(1 + -3t)

Combine like terms: -2 + -1 = -3
-3 + 7t + 3t = -3t(1 + -3t)

Combine like terms: 7t + 3t = 10t
-3 + 10t = -3t(1 + -3t)
-3 + 10t = (1 * -3t + -3t * -3t)
-3 + 10t = (-3t + 9t2)

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

Solving for variable 't'.

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

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

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

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

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

Divide each side by '-9'.
0.3333333333 + -1.444444444t + t2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1.444444444t + -0.3333333333 + t2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1.444444444t + t2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1.444444444t + t2 = 0 + -0.3333333333
-1.444444444t + t2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1.444444444t + t2 = -0.3333333333

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 = -0.3333333333 + 0.5216049380

Reorder the terms:
0.5216049380 + -1.444444444t + t2 = -0.3333333333 + 0.5216049380

Combine like terms: -0.3333333333 + 0.5216049380 = 0.1882716047
0.5216049380 + -1.444444444t + t2 = 0.1882716047

Factor a perfect square on the left side:
(t + -0.722222222)(t + -0.722222222) = 0.1882716047

Calculate the square root of the right side: 0.433902759

Break this problem into two subproblems by setting 
(t + -0.722222222) equal to 0.433902759 and -0.433902759.

Subproblem 1
t + -0.722222222 = 0.433902759

Simplifying
t + -0.722222222 = 0.433902759

Reorder the terms:
-0.722222222 + t = 0.433902759

Solving
-0.722222222 + t = 0.433902759

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 = 0.433902759 + 0.722222222

Combine like terms: -0.722222222 + 0.722222222 = 0.000000000
0.000000000 + t = 0.433902759 + 0.722222222
t = 0.433902759 + 0.722222222

Combine like terms: 0.433902759 + 0.722222222 = 1.156124981
t = 1.156124981

Simplifying
t = 1.156124981

Subproblem 2
t + -0.722222222 = -0.433902759

Simplifying
t + -0.722222222 = -0.433902759

Reorder the terms:
-0.722222222 + t = -0.433902759

Solving
-0.722222222 + t = -0.433902759

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 = -0.433902759 + 0.722222222

Combine like terms: -0.722222222 + 0.722222222 = 0.000000000
0.000000000 + t = -0.433902759 + 0.722222222
t = -0.433902759 + 0.722222222

Combine like terms: -0.433902759 + 0.722222222 = 0.288319463
t = 0.288319463

Simplifying
t = 0.288319463

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.156124981, 0.288319463}