9t-21=3(t-7)6t

Solution for 9t-21=3(t-7)6t equation:

Simplifying
9t + -21 = 3(t + -7) * 6t

Reorder the terms:
-21 + 9t = 3(t + -7) * 6t

Reorder the terms:
-21 + 9t = 3(-7 + t) * 6t

Reorder the terms for easier multiplication:
-21 + 9t = 3 * 6t(-7 + t)

Multiply 3 * 6
-21 + 9t = 18t(-7 + t)
-21 + 9t = (-7 * 18t + t * 18t)
-21 + 9t = (-126t + 18t2)

Solving
-21 + 9t = -126t + 18t2

Solving for variable 't'.

Combine like terms: 9t + 126t = 135t
-21 + 135t + -18t2 = -126t + 18t2 + 126t + -18t2

Reorder the terms:
-21 + 135t + -18t2 = -126t + 126t + 18t2 + -18t2

Combine like terms: -126t + 126t = 0
-21 + 135t + -18t2 = 0 + 18t2 + -18t2
-21 + 135t + -18t2 = 18t2 + -18t2

Combine like terms: 18t2 + -18t2 = 0
-21 + 135t + -18t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 45t + -6t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + 45t + -6t2)' equal to zero and attempt to solve:

Simplifying
-7 + 45t + -6t2 = 0

Solving
-7 + 45t + -6t2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
1.166666667 + -7.5t + t2 = 0

Move the constant term to the right:

Add '-1.166666667' to each side of the equation.
1.166666667 + -7.5t + -1.166666667 + t2 = 0 + -1.166666667

Reorder the terms:
1.166666667 + -1.166666667 + -7.5t + t2 = 0 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + -7.5t + t2 = 0 + -1.166666667
-7.5t + t2 = 0 + -1.166666667

Combine like terms: 0 + -1.166666667 = -1.166666667
-7.5t + t2 = -1.166666667

The t term is -7.5t.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5t + 14.0625 + t2 = -1.166666667 + 14.0625

Reorder the terms:
14.0625 + -7.5t + t2 = -1.166666667 + 14.0625

Combine like terms: -1.166666667 + 14.0625 = 12.895833333
14.0625 + -7.5t + t2 = 12.895833333

Factor a perfect square on the left side:
(t + -3.75)(t + -3.75) = 12.895833333

Calculate the square root of the right side: 3.591076904

Break this problem into two subproblems by setting 
(t + -3.75) equal to 3.591076904 and -3.591076904.

Subproblem 1
t + -3.75 = 3.591076904

Simplifying
t + -3.75 = 3.591076904

Reorder the terms:
-3.75 + t = 3.591076904

Solving
-3.75 + t = 3.591076904

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = 3.591076904 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = 3.591076904 + 3.75
t = 3.591076904 + 3.75

Combine like terms: 3.591076904 + 3.75 = 7.341076904
t = 7.341076904

Simplifying
t = 7.341076904

Subproblem 2
t + -3.75 = -3.591076904

Simplifying
t + -3.75 = -3.591076904

Reorder the terms:
-3.75 + t = -3.591076904

Solving
-3.75 + t = -3.591076904

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = -3.591076904 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = -3.591076904 + 3.75
t = -3.591076904 + 3.75

Combine like terms: -3.591076904 + 3.75 = 0.158923096
t = 0.158923096

Simplifying
t = 0.158923096

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.341076904, 0.158923096}
Solution
t = {7.341076904, 0.158923096}