4(t-4)6t=5(2t+3)-10

Solution for 4(t-4)6t=5(2t+3)-10 equation:

Simplifying
4(t + -4) * 6t = 5(2t + 3) + -10

Reorder the terms:
4(-4 + t) * 6t = 5(2t + 3) + -10

Reorder the terms for easier multiplication:
4 * 6t(-4 + t) = 5(2t + 3) + -10

Multiply 4 * 6
24t(-4 + t) = 5(2t + 3) + -10
(-4 * 24t + t * 24t) = 5(2t + 3) + -10
(-96t + 24t2) = 5(2t + 3) + -10

Reorder the terms:
-96t + 24t2 = 5(3 + 2t) + -10
-96t + 24t2 = (3 * 5 + 2t * 5) + -10
-96t + 24t2 = (15 + 10t) + -10

Reorder the terms:
-96t + 24t2 = 15 + -10 + 10t

Combine like terms: 15 + -10 = 5
-96t + 24t2 = 5 + 10t

Solving
-96t + 24t2 = 5 + 10t

Solving for variable 't'.

Reorder the terms:
-5 + -96t + -10t + 24t2 = 5 + 10t + -5 + -10t

Combine like terms: -96t + -10t = -106t
-5 + -106t + 24t2 = 5 + 10t + -5 + -10t

Reorder the terms:
-5 + -106t + 24t2 = 5 + -5 + 10t + -10t

Combine like terms: 5 + -5 = 0
-5 + -106t + 24t2 = 0 + 10t + -10t
-5 + -106t + 24t2 = 10t + -10t

Combine like terms: 10t + -10t = 0
-5 + -106t + 24t2 = 0

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

Divide each side by '24'.
-0.2083333333 + -4.416666667t + t2 = 0

Move the constant term to the right:

Add '0.2083333333' to each side of the equation.
-0.2083333333 + -4.416666667t + 0.2083333333 + t2 = 0 + 0.2083333333

Reorder the terms:
-0.2083333333 + 0.2083333333 + -4.416666667t + t2 = 0 + 0.2083333333

Combine like terms: -0.2083333333 + 0.2083333333 = 0.0000000000
0.0000000000 + -4.416666667t + t2 = 0 + 0.2083333333
-4.416666667t + t2 = 0 + 0.2083333333

Combine like terms: 0 + 0.2083333333 = 0.2083333333
-4.416666667t + t2 = 0.2083333333

The t term is -4.416666667t.  Take half its coefficient (-2.208333334).
Square it (4.876736114) and add it to both sides.

Add '4.876736114' to each side of the equation.
-4.416666667t + 4.876736114 + t2 = 0.2083333333 + 4.876736114

Reorder the terms:
4.876736114 + -4.416666667t + t2 = 0.2083333333 + 4.876736114

Combine like terms: 0.2083333333 + 4.876736114 = 5.0850694473
4.876736114 + -4.416666667t + t2 = 5.0850694473

Factor a perfect square on the left side:
(t + -2.208333334)(t + -2.208333334) = 5.0850694473

Calculate the square root of the right side: 2.255009855

Break this problem into two subproblems by setting 
(t + -2.208333334) equal to 2.255009855 and -2.255009855.

Subproblem 1
t + -2.208333334 = 2.255009855

Simplifying
t + -2.208333334 = 2.255009855

Reorder the terms:
-2.208333334 + t = 2.255009855

Solving
-2.208333334 + t = 2.255009855

Solving for variable 't'.

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

Add '2.208333334' to each side of the equation.
-2.208333334 + 2.208333334 + t = 2.255009855 + 2.208333334

Combine like terms: -2.208333334 + 2.208333334 = 0.000000000
0.000000000 + t = 2.255009855 + 2.208333334
t = 2.255009855 + 2.208333334

Combine like terms: 2.255009855 + 2.208333334 = 4.463343189
t = 4.463343189

Simplifying
t = 4.463343189

Subproblem 2
t + -2.208333334 = -2.255009855

Simplifying
t + -2.208333334 = -2.255009855

Reorder the terms:
-2.208333334 + t = -2.255009855

Solving
-2.208333334 + t = -2.255009855

Solving for variable 't'.

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

Add '2.208333334' to each side of the equation.
-2.208333334 + 2.208333334 + t = -2.255009855 + 2.208333334

Combine like terms: -2.208333334 + 2.208333334 = 0.000000000
0.000000000 + t = -2.255009855 + 2.208333334
t = -2.255009855 + 2.208333334

Combine like terms: -2.255009855 + 2.208333334 = -0.046676521
t = -0.046676521

Simplifying
t = -0.046676521

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.463343189, -0.046676521}