-3t(8+7t)=2t+2(4t-53-t)

Solution for -3t(8+7t)=2t+2(4t-53-t) equation:

Simplifying
-3t(8 + 7t) = 2t + 2(4t + -53 + -1t)
(8 * -3t + 7t * -3t) = 2t + 2(4t + -53 + -1t)
(-24t + -21t2) = 2t + 2(4t + -53 + -1t)

Reorder the terms:
-24t + -21t2 = 2t + 2(-53 + 4t + -1t)

Combine like terms: 4t + -1t = 3t
-24t + -21t2 = 2t + 2(-53 + 3t)
-24t + -21t2 = 2t + (-53 * 2 + 3t * 2)
-24t + -21t2 = 2t + (-106 + 6t)

Reorder the terms:
-24t + -21t2 = -106 + 2t + 6t

Combine like terms: 2t + 6t = 8t
-24t + -21t2 = -106 + 8t

Solving
-24t + -21t2 = -106 + 8t

Solving for variable 't'.

Reorder the terms:
106 + -24t + -8t + -21t2 = -106 + 8t + 106 + -8t

Combine like terms: -24t + -8t = -32t
106 + -32t + -21t2 = -106 + 8t + 106 + -8t

Reorder the terms:
106 + -32t + -21t2 = -106 + 106 + 8t + -8t

Combine like terms: -106 + 106 = 0
106 + -32t + -21t2 = 0 + 8t + -8t
106 + -32t + -21t2 = 8t + -8t

Combine like terms: 8t + -8t = 0
106 + -32t + -21t2 = 0

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

Divide each side by '-21'.
-5.047619048 + 1.523809524t + t2 = 0

Move the constant term to the right:

Add '5.047619048' to each side of the equation.
-5.047619048 + 1.523809524t + 5.047619048 + t2 = 0 + 5.047619048

Reorder the terms:
-5.047619048 + 5.047619048 + 1.523809524t + t2 = 0 + 5.047619048

Combine like terms: -5.047619048 + 5.047619048 = 0.000000000
0.000000000 + 1.523809524t + t2 = 0 + 5.047619048
1.523809524t + t2 = 0 + 5.047619048

Combine like terms: 0 + 5.047619048 = 5.047619048
1.523809524t + t2 = 5.047619048

The t term is 1.523809524t.  Take half its coefficient (0.761904762).
Square it (0.5804988664) and add it to both sides.

Add '0.5804988664' to each side of the equation.
1.523809524t + 0.5804988664 + t2 = 5.047619048 + 0.5804988664

Reorder the terms:
0.5804988664 + 1.523809524t + t2 = 5.047619048 + 0.5804988664

Combine like terms: 5.047619048 + 0.5804988664 = 5.6281179144
0.5804988664 + 1.523809524t + t2 = 5.6281179144

Factor a perfect square on the left side:
(t + 0.761904762)(t + 0.761904762) = 5.6281179144

Calculate the square root of the right side: 2.372365468

Break this problem into two subproblems by setting 
(t + 0.761904762) equal to 2.372365468 and -2.372365468.

Subproblem 1
t + 0.761904762 = 2.372365468

Simplifying
t + 0.761904762 = 2.372365468

Reorder the terms:
0.761904762 + t = 2.372365468

Solving
0.761904762 + t = 2.372365468

Solving for variable 't'.

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

Add '-0.761904762' to each side of the equation.
0.761904762 + -0.761904762 + t = 2.372365468 + -0.761904762

Combine like terms: 0.761904762 + -0.761904762 = 0.000000000
0.000000000 + t = 2.372365468 + -0.761904762
t = 2.372365468 + -0.761904762

Combine like terms: 2.372365468 + -0.761904762 = 1.610460706
t = 1.610460706

Simplifying
t = 1.610460706

Subproblem 2
t + 0.761904762 = -2.372365468

Simplifying
t + 0.761904762 = -2.372365468

Reorder the terms:
0.761904762 + t = -2.372365468

Solving
0.761904762 + t = -2.372365468

Solving for variable 't'.

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

Add '-0.761904762' to each side of the equation.
0.761904762 + -0.761904762 + t = -2.372365468 + -0.761904762

Combine like terms: 0.761904762 + -0.761904762 = 0.000000000
0.000000000 + t = -2.372365468 + -0.761904762
t = -2.372365468 + -0.761904762

Combine like terms: -2.372365468 + -0.761904762 = -3.13427023
t = -3.13427023

Simplifying
t = -3.13427023

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.610460706, -3.13427023}