3(t-5)7t=5(3-t)

Solution for 3(t-5)7t=5(3-t) equation:

Simplifying
3(t + -5) * 7t = 5(3 + -1t)

Reorder the terms:
3(-5 + t) * 7t = 5(3 + -1t)

Reorder the terms for easier multiplication:
3 * 7t(-5 + t) = 5(3 + -1t)

Multiply 3 * 7
21t(-5 + t) = 5(3 + -1t)
(-5 * 21t + t * 21t) = 5(3 + -1t)
(-105t + 21t2) = 5(3 + -1t)
-105t + 21t2 = (3 * 5 + -1t * 5)
-105t + 21t2 = (15 + -5t)

Solving
-105t + 21t2 = 15 + -5t

Solving for variable 't'.

Reorder the terms:
-15 + -105t + 5t + 21t2 = 15 + -5t + -15 + 5t

Combine like terms: -105t + 5t = -100t
-15 + -100t + 21t2 = 15 + -5t + -15 + 5t

Reorder the terms:
-15 + -100t + 21t2 = 15 + -15 + -5t + 5t

Combine like terms: 15 + -15 = 0
-15 + -100t + 21t2 = 0 + -5t + 5t
-15 + -100t + 21t2 = -5t + 5t

Combine like terms: -5t + 5t = 0
-15 + -100t + 21t2 = 0

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

Divide each side by '21'.
-0.7142857143 + -4.761904762t + t2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + -4.761904762t + 0.7142857143 + t2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + -4.761904762t + t2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + -4.761904762t + t2 = 0 + 0.7142857143
-4.761904762t + t2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
-4.761904762t + t2 = 0.7142857143

The t term is -4.761904762t.  Take half its coefficient (-2.380952381).
Square it (5.668934241) and add it to both sides.

Add '5.668934241' to each side of the equation.
-4.761904762t + 5.668934241 + t2 = 0.7142857143 + 5.668934241

Reorder the terms:
5.668934241 + -4.761904762t + t2 = 0.7142857143 + 5.668934241

Combine like terms: 0.7142857143 + 5.668934241 = 6.3832199553
5.668934241 + -4.761904762t + t2 = 6.3832199553

Factor a perfect square on the left side:
(t + -2.380952381)(t + -2.380952381) = 6.3832199553

Calculate the square root of the right side: 2.526503504

Break this problem into two subproblems by setting 
(t + -2.380952381) equal to 2.526503504 and -2.526503504.

Subproblem 1
t + -2.380952381 = 2.526503504

Simplifying
t + -2.380952381 = 2.526503504

Reorder the terms:
-2.380952381 + t = 2.526503504

Solving
-2.380952381 + t = 2.526503504

Solving for variable 't'.

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

Add '2.380952381' to each side of the equation.
-2.380952381 + 2.380952381 + t = 2.526503504 + 2.380952381

Combine like terms: -2.380952381 + 2.380952381 = 0.000000000
0.000000000 + t = 2.526503504 + 2.380952381
t = 2.526503504 + 2.380952381

Combine like terms: 2.526503504 + 2.380952381 = 4.907455885
t = 4.907455885

Simplifying
t = 4.907455885

Subproblem 2
t + -2.380952381 = -2.526503504

Simplifying
t + -2.380952381 = -2.526503504

Reorder the terms:
-2.380952381 + t = -2.526503504

Solving
-2.380952381 + t = -2.526503504

Solving for variable 't'.

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

Add '2.380952381' to each side of the equation.
-2.380952381 + 2.380952381 + t = -2.526503504 + 2.380952381

Combine like terms: -2.380952381 + 2.380952381 = 0.000000000
0.000000000 + t = -2.526503504 + 2.380952381
t = -2.526503504 + 2.380952381

Combine like terms: -2.526503504 + 2.380952381 = -0.145551123
t = -0.145551123

Simplifying
t = -0.145551123

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.907455885, -0.145551123}