4t-(12t-24)38t-38=0

Solution for 4t-(12t-24)38t-38=0 equation:

Simplifying
4t + -1(12t + -24) * 38t + -38 = 0

Reorder the terms:
4t + -1(-24 + 12t) * 38t + -38 = 0

Reorder the terms for easier multiplication:
4t + -1 * 38t(-24 + 12t) + -38 = 0

Multiply -1 * 38
4t + -38t(-24 + 12t) + -38 = 0
4t + (-24 * -38t + 12t * -38t) + -38 = 0
4t + (912t + -456t2) + -38 = 0

Reorder the terms:
-38 + 4t + 912t + -456t2 = 0

Combine like terms: 4t + 912t = 916t
-38 + 916t + -456t2 = 0

Solving
-38 + 916t + -456t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + 458t + -228t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-19 + 458t + -228t2)' equal to zero and attempt to solve:

Simplifying
-19 + 458t + -228t2 = 0

Solving
-19 + 458t + -228t2 = 0

Begin completing the square.  Divide all terms by
-228 the coefficient of the squared term: 

Divide each side by '-228'.
0.08333333333 + -2.00877193t + t2 = 0

Move the constant term to the right:

Add '-0.08333333333' to each side of the equation.
0.08333333333 + -2.00877193t + -0.08333333333 + t2 = 0 + -0.08333333333

Reorder the terms:
0.08333333333 + -0.08333333333 + -2.00877193t + t2 = 0 + -0.08333333333

Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000
0.00000000000 + -2.00877193t + t2 = 0 + -0.08333333333
-2.00877193t + t2 = 0 + -0.08333333333

Combine like terms: 0 + -0.08333333333 = -0.08333333333
-2.00877193t + t2 = -0.08333333333

The t term is -2.00877193t.  Take half its coefficient (-1.004385965).
Square it (1.008791167) and add it to both sides.

Add '1.008791167' to each side of the equation.
-2.00877193t + 1.008791167 + t2 = -0.08333333333 + 1.008791167

Reorder the terms:
1.008791167 + -2.00877193t + t2 = -0.08333333333 + 1.008791167

Combine like terms: -0.08333333333 + 1.008791167 = 0.92545783367
1.008791167 + -2.00877193t + t2 = 0.92545783367

Factor a perfect square on the left side:
(t + -1.004385965)(t + -1.004385965) = 0.92545783367

Calculate the square root of the right side: 0.96200719

Break this problem into two subproblems by setting 
(t + -1.004385965) equal to 0.96200719 and -0.96200719.

Subproblem 1
t + -1.004385965 = 0.96200719

Simplifying
t + -1.004385965 = 0.96200719

Reorder the terms:
-1.004385965 + t = 0.96200719

Solving
-1.004385965 + t = 0.96200719

Solving for variable 't'.

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

Add '1.004385965' to each side of the equation.
-1.004385965 + 1.004385965 + t = 0.96200719 + 1.004385965

Combine like terms: -1.004385965 + 1.004385965 = 0.000000000
0.000000000 + t = 0.96200719 + 1.004385965
t = 0.96200719 + 1.004385965

Combine like terms: 0.96200719 + 1.004385965 = 1.966393155
t = 1.966393155

Simplifying
t = 1.966393155

Subproblem 2
t + -1.004385965 = -0.96200719

Simplifying
t + -1.004385965 = -0.96200719

Reorder the terms:
-1.004385965 + t = -0.96200719

Solving
-1.004385965 + t = -0.96200719

Solving for variable 't'.

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

Add '1.004385965' to each side of the equation.
-1.004385965 + 1.004385965 + t = -0.96200719 + 1.004385965

Combine like terms: -1.004385965 + 1.004385965 = 0.000000000
0.000000000 + t = -0.96200719 + 1.004385965
t = -0.96200719 + 1.004385965

Combine like terms: -0.96200719 + 1.004385965 = 0.042378775
t = 0.042378775

Simplifying
t = 0.042378775

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.966393155, 0.042378775}
Solution
t = {1.966393155, 0.042378775}