4(3t-4)-((t^2)+3)-3t(t-5)=

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

Simplifying
4(3t + -4) + -1((t2) + 3) + -3t(t + -5) = 0

Reorder the terms:
4(-4 + 3t) + -1((t2) + 3) + -3t(t + -5) = 0
(-4 * 4 + 3t * 4) + -1((t2) + 3) + -3t(t + -5) = 0
(-16 + 12t) + -1((t2) + 3) + -3t(t + -5) = 0
-16 + 12t + -1(t2 + 3) + -3t(t + -5) = 0

Reorder the terms:
-16 + 12t + -1(3 + t2) + -3t(t + -5) = 0
-16 + 12t + (3 * -1 + t2 * -1) + -3t(t + -5) = 0
-16 + 12t + (-3 + -1t2) + -3t(t + -5) = 0

Reorder the terms:
-16 + 12t + -3 + -1t2 + -3t(-5 + t) = 0
-16 + 12t + -3 + -1t2 + (-5 * -3t + t * -3t) = 0
-16 + 12t + -3 + -1t2 + (15t + -3t2) = 0

Reorder the terms:
-16 + -3 + 12t + 15t + -1t2 + -3t2 = 0

Combine like terms: -16 + -3 = -19
-19 + 12t + 15t + -1t2 + -3t2 = 0

Combine like terms: 12t + 15t = 27t
-19 + 27t + -1t2 + -3t2 = 0

Combine like terms: -1t2 + -3t2 = -4t2
-19 + 27t + -4t2 = 0

Solving
-19 + 27t + -4t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
4.75 + -6.75t + t2 = 0

Move the constant term to the right:

Add '-4.75' to each side of the equation.
4.75 + -6.75t + -4.75 + t2 = 0 + -4.75

Reorder the terms:
4.75 + -4.75 + -6.75t + t2 = 0 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + -6.75t + t2 = 0 + -4.75
-6.75t + t2 = 0 + -4.75

Combine like terms: 0 + -4.75 = -4.75
-6.75t + t2 = -4.75

The t term is -6.75t.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75t + 11.390625 + t2 = -4.75 + 11.390625

Reorder the terms:
11.390625 + -6.75t + t2 = -4.75 + 11.390625

Combine like terms: -4.75 + 11.390625 = 6.640625
11.390625 + -6.75t + t2 = 6.640625

Factor a perfect square on the left side:
(t + -3.375)(t + -3.375) = 6.640625

Calculate the square root of the right side: 2.576941016

Break this problem into two subproblems by setting 
(t + -3.375) equal to 2.576941016 and -2.576941016.

Subproblem 1
t + -3.375 = 2.576941016

Simplifying
t + -3.375 = 2.576941016

Reorder the terms:
-3.375 + t = 2.576941016

Solving
-3.375 + t = 2.576941016

Solving for variable 't'.

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

Add '3.375' to each side of the equation.
-3.375 + 3.375 + t = 2.576941016 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
0.000 + t = 2.576941016 + 3.375
t = 2.576941016 + 3.375

Combine like terms: 2.576941016 + 3.375 = 5.951941016
t = 5.951941016

Simplifying
t = 5.951941016

Subproblem 2
t + -3.375 = -2.576941016

Simplifying
t + -3.375 = -2.576941016

Reorder the terms:
-3.375 + t = -2.576941016

Solving
-3.375 + t = -2.576941016

Solving for variable 't'.

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

Add '3.375' to each side of the equation.
-3.375 + 3.375 + t = -2.576941016 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
0.000 + t = -2.576941016 + 3.375
t = -2.576941016 + 3.375

Combine like terms: -2.576941016 + 3.375 = 0.798058984
t = 0.798058984

Simplifying
t = 0.798058984

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.951941016, 0.798058984}