-4t(3t-9)=8(-8-t)

Solution for -4t(3t-9)=8(-8-t) equation:

Simplifying
-4t(3t + -9) = 8(-8 + -1t)

Reorder the terms:
-4t(-9 + 3t) = 8(-8 + -1t)
(-9 * -4t + 3t * -4t) = 8(-8 + -1t)
(36t + -12t2) = 8(-8 + -1t)
36t + -12t2 = (-8 * 8 + -1t * 8)
36t + -12t2 = (-64 + -8t)

Solving
36t + -12t2 = -64 + -8t

Solving for variable 't'.

Reorder the terms:
64 + 36t + 8t + -12t2 = -64 + -8t + 64 + 8t

Combine like terms: 36t + 8t = 44t
64 + 44t + -12t2 = -64 + -8t + 64 + 8t

Reorder the terms:
64 + 44t + -12t2 = -64 + 64 + -8t + 8t

Combine like terms: -64 + 64 = 0
64 + 44t + -12t2 = 0 + -8t + 8t
64 + 44t + -12t2 = -8t + 8t

Combine like terms: -8t + 8t = 0
64 + 44t + -12t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + 11t + -3t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(16 + 11t + -3t2)' equal to zero and attempt to solve:

Simplifying
16 + 11t + -3t2 = 0

Solving
16 + 11t + -3t2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-5.333333333 + -3.666666667t + t2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -3.666666667t + 5.333333333 + t2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -3.666666667t + t2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -3.666666667t + t2 = 0 + 5.333333333
-3.666666667t + t2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-3.666666667t + t2 = 5.333333333

The t term is -3.666666667t.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667t + 3.361111114 + t2 = 5.333333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667t + t2 = 5.333333333 + 3.361111114

Combine like terms: 5.333333333 + 3.361111114 = 8.694444447
3.361111114 + -3.666666667t + t2 = 8.694444447

Factor a perfect square on the left side:
(t + -1.833333334)(t + -1.833333334) = 8.694444447

Calculate the square root of the right side: 2.948634336

Break this problem into two subproblems by setting 
(t + -1.833333334) equal to 2.948634336 and -2.948634336.

Subproblem 1
t + -1.833333334 = 2.948634336

Simplifying
t + -1.833333334 = 2.948634336

Reorder the terms:
-1.833333334 + t = 2.948634336

Solving
-1.833333334 + t = 2.948634336

Solving for variable 't'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + t = 2.948634336 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + t = 2.948634336 + 1.833333334
t = 2.948634336 + 1.833333334

Combine like terms: 2.948634336 + 1.833333334 = 4.78196767
t = 4.78196767

Simplifying
t = 4.78196767

Subproblem 2
t + -1.833333334 = -2.948634336

Simplifying
t + -1.833333334 = -2.948634336

Reorder the terms:
-1.833333334 + t = -2.948634336

Solving
-1.833333334 + t = -2.948634336

Solving for variable 't'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + t = -2.948634336 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + t = -2.948634336 + 1.833333334
t = -2.948634336 + 1.833333334

Combine like terms: -2.948634336 + 1.833333334 = -1.115301002
t = -1.115301002

Simplifying
t = -1.115301002

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.78196767, -1.115301002}
Solution
t = {4.78196767, -1.115301002}