14(t-6)7t=7(3t+4)-8

Solution for 14(t-6)7t=7(3t+4)-8 equation:

Simplifying
14(t + -6) * 7t = 7(3t + 4) + -8

Reorder the terms:
14(-6 + t) * 7t = 7(3t + 4) + -8

Reorder the terms for easier multiplication:
14 * 7t(-6 + t) = 7(3t + 4) + -8

Multiply 14 * 7
98t(-6 + t) = 7(3t + 4) + -8
(-6 * 98t + t * 98t) = 7(3t + 4) + -8
(-588t + 98t2) = 7(3t + 4) + -8

Reorder the terms:
-588t + 98t2 = 7(4 + 3t) + -8
-588t + 98t2 = (4 * 7 + 3t * 7) + -8
-588t + 98t2 = (28 + 21t) + -8

Reorder the terms:
-588t + 98t2 = 28 + -8 + 21t

Combine like terms: 28 + -8 = 20
-588t + 98t2 = 20 + 21t

Solving
-588t + 98t2 = 20 + 21t

Solving for variable 't'.

Reorder the terms:
-20 + -588t + -21t + 98t2 = 20 + 21t + -20 + -21t

Combine like terms: -588t + -21t = -609t
-20 + -609t + 98t2 = 20 + 21t + -20 + -21t

Reorder the terms:
-20 + -609t + 98t2 = 20 + -20 + 21t + -21t

Combine like terms: 20 + -20 = 0
-20 + -609t + 98t2 = 0 + 21t + -21t
-20 + -609t + 98t2 = 21t + -21t

Combine like terms: 21t + -21t = 0
-20 + -609t + 98t2 = 0

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

Divide each side by '98'.
-0.2040816327 + -6.214285714t + t2 = 0

Move the constant term to the right:

Add '0.2040816327' to each side of the equation.
-0.2040816327 + -6.214285714t + 0.2040816327 + t2 = 0 + 0.2040816327

Reorder the terms:
-0.2040816327 + 0.2040816327 + -6.214285714t + t2 = 0 + 0.2040816327

Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000
0.0000000000 + -6.214285714t + t2 = 0 + 0.2040816327
-6.214285714t + t2 = 0 + 0.2040816327

Combine like terms: 0 + 0.2040816327 = 0.2040816327
-6.214285714t + t2 = 0.2040816327

The t term is -6.214285714t.  Take half its coefficient (-3.107142857).
Square it (9.654336734) and add it to both sides.

Add '9.654336734' to each side of the equation.
-6.214285714t + 9.654336734 + t2 = 0.2040816327 + 9.654336734

Reorder the terms:
9.654336734 + -6.214285714t + t2 = 0.2040816327 + 9.654336734

Combine like terms: 0.2040816327 + 9.654336734 = 9.8584183667
9.654336734 + -6.214285714t + t2 = 9.8584183667

Factor a perfect square on the left side:
(t + -3.107142857)(t + -3.107142857) = 9.8584183667

Calculate the square root of the right side: 3.139811836

Break this problem into two subproblems by setting 
(t + -3.107142857) equal to 3.139811836 and -3.139811836.

Subproblem 1
t + -3.107142857 = 3.139811836

Simplifying
t + -3.107142857 = 3.139811836

Reorder the terms:
-3.107142857 + t = 3.139811836

Solving
-3.107142857 + t = 3.139811836

Solving for variable 't'.

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

Add '3.107142857' to each side of the equation.
-3.107142857 + 3.107142857 + t = 3.139811836 + 3.107142857

Combine like terms: -3.107142857 + 3.107142857 = 0.000000000
0.000000000 + t = 3.139811836 + 3.107142857
t = 3.139811836 + 3.107142857

Combine like terms: 3.139811836 + 3.107142857 = 6.246954693
t = 6.246954693

Simplifying
t = 6.246954693

Subproblem 2
t + -3.107142857 = -3.139811836

Simplifying
t + -3.107142857 = -3.139811836

Reorder the terms:
-3.107142857 + t = -3.139811836

Solving
-3.107142857 + t = -3.139811836

Solving for variable 't'.

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

Add '3.107142857' to each side of the equation.
-3.107142857 + 3.107142857 + t = -3.139811836 + 3.107142857

Combine like terms: -3.107142857 + 3.107142857 = 0.000000000
0.000000000 + t = -3.139811836 + 3.107142857
t = -3.139811836 + 3.107142857

Combine like terms: -3.139811836 + 3.107142857 = -0.032668979
t = -0.032668979

Simplifying
t = -0.032668979

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.246954693, -0.032668979}