8(t+2)3(t-4)=6(t-7)+8

Solution for 8(t+2)3(t-4)=6(t-7)+8 equation:

Simplifying
8(t + 2) * 3(t + -4) = 6(t + -7) + 8

Reorder the terms:
8(2 + t) * 3(t + -4) = 6(t + -7) + 8

Reorder the terms:
8(2 + t) * 3(-4 + t) = 6(t + -7) + 8

Reorder the terms for easier multiplication:
8 * 3(2 + t)(-4 + t) = 6(t + -7) + 8

Multiply 8 * 3
24(2 + t)(-4 + t) = 6(t + -7) + 8

Multiply (2 + t) * (-4 + t)
24(2(-4 + t) + t(-4 + t)) = 6(t + -7) + 8
24((-4 * 2 + t * 2) + t(-4 + t)) = 6(t + -7) + 8
24((-8 + 2t) + t(-4 + t)) = 6(t + -7) + 8
24(-8 + 2t + (-4 * t + t * t)) = 6(t + -7) + 8
24(-8 + 2t + (-4t + t2)) = 6(t + -7) + 8

Combine like terms: 2t + -4t = -2t
24(-8 + -2t + t2) = 6(t + -7) + 8
(-8 * 24 + -2t * 24 + t2 * 24) = 6(t + -7) + 8
(-192 + -48t + 24t2) = 6(t + -7) + 8

Reorder the terms:
-192 + -48t + 24t2 = 6(-7 + t) + 8
-192 + -48t + 24t2 = (-7 * 6 + t * 6) + 8
-192 + -48t + 24t2 = (-42 + 6t) + 8

Reorder the terms:
-192 + -48t + 24t2 = -42 + 8 + 6t

Combine like terms: -42 + 8 = -34
-192 + -48t + 24t2 = -34 + 6t

Solving
-192 + -48t + 24t2 = -34 + 6t

Solving for variable 't'.

Reorder the terms:
-192 + 34 + -48t + -6t + 24t2 = -34 + 6t + 34 + -6t

Combine like terms: -192 + 34 = -158
-158 + -48t + -6t + 24t2 = -34 + 6t + 34 + -6t

Combine like terms: -48t + -6t = -54t
-158 + -54t + 24t2 = -34 + 6t + 34 + -6t

Reorder the terms:
-158 + -54t + 24t2 = -34 + 34 + 6t + -6t

Combine like terms: -34 + 34 = 0
-158 + -54t + 24t2 = 0 + 6t + -6t
-158 + -54t + 24t2 = 6t + -6t

Combine like terms: 6t + -6t = 0
-158 + -54t + 24t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-79 + -27t + 12t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-79 + -27t + 12t2)' equal to zero and attempt to solve:

Simplifying
-79 + -27t + 12t2 = 0

Solving
-79 + -27t + 12t2 = 0

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

Divide each side by '12'.
-6.583333333 + -2.25t + t2 = 0

Move the constant term to the right:

Add '6.583333333' to each side of the equation.
-6.583333333 + -2.25t + 6.583333333 + t2 = 0 + 6.583333333

Reorder the terms:
-6.583333333 + 6.583333333 + -2.25t + t2 = 0 + 6.583333333

Combine like terms: -6.583333333 + 6.583333333 = 0.000000000
0.000000000 + -2.25t + t2 = 0 + 6.583333333
-2.25t + t2 = 0 + 6.583333333

Combine like terms: 0 + 6.583333333 = 6.583333333
-2.25t + t2 = 6.583333333

The t term is -2.25t.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25t + 1.265625 + t2 = 6.583333333 + 1.265625

Reorder the terms:
1.265625 + -2.25t + t2 = 6.583333333 + 1.265625

Combine like terms: 6.583333333 + 1.265625 = 7.848958333
1.265625 + -2.25t + t2 = 7.848958333

Factor a perfect square on the left side:
(t + -1.125)(t + -1.125) = 7.848958333

Calculate the square root of the right side: 2.801599246

Break this problem into two subproblems by setting 
(t + -1.125) equal to 2.801599246 and -2.801599246.

Subproblem 1
t + -1.125 = 2.801599246

Simplifying
t + -1.125 = 2.801599246

Reorder the terms:
-1.125 + t = 2.801599246

Solving
-1.125 + t = 2.801599246

Solving for variable 't'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + t = 2.801599246 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + t = 2.801599246 + 1.125
t = 2.801599246 + 1.125

Combine like terms: 2.801599246 + 1.125 = 3.926599246
t = 3.926599246

Simplifying
t = 3.926599246

Subproblem 2
t + -1.125 = -2.801599246

Simplifying
t + -1.125 = -2.801599246

Reorder the terms:
-1.125 + t = -2.801599246

Solving
-1.125 + t = -2.801599246

Solving for variable 't'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + t = -2.801599246 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + t = -2.801599246 + 1.125
t = -2.801599246 + 1.125

Combine like terms: -2.801599246 + 1.125 = -1.676599246
t = -1.676599246

Simplifying
t = -1.676599246

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.926599246, -1.676599246}
Solution
t = {3.926599246, -1.676599246}