3t^2-48t+33=0

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Solution for 3t^2-48t+33=0 equation:


Simplifying
3t2 + -48t + 33 = 0

Reorder the terms:
33 + -48t + 3t2 = 0

Solving
33 + -48t + 3t2 = 0

Solving for variable 't'.

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

Ignore the factor 3.

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

Simplifying
11 + -16t + t2 = 0

Solving
11 + -16t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -16t + -11 + t2 = 0 + -11

Reorder the terms:
11 + -11 + -16t + t2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -16t + t2 = 0 + -11
-16t + t2 = 0 + -11

Combine like terms: 0 + -11 = -11
-16t + t2 = -11

The t term is -16t.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16t + 64 + t2 = -11 + 64

Reorder the terms:
64 + -16t + t2 = -11 + 64

Combine like terms: -11 + 64 = 53
64 + -16t + t2 = 53

Factor a perfect square on the left side:
(t + -8)(t + -8) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(t + -8) equal to 7.280109889 and -7.280109889.


Subproblem 1
t + -8 = 7.280109889

Simplifying
t + -8 = 7.280109889

Reorder the terms:
-8 + t = 7.280109889

Solving
-8 + t = 7.280109889

Solving for variable 't'.

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

Add '8' to each side of the equation.
-8 + 8 + t = 7.280109889 + 8

Combine like terms: -8 + 8 = 0
0 + t = 7.280109889 + 8
t = 7.280109889 + 8

Combine like terms: 7.280109889 + 8 = 15.280109889
t = 15.280109889

Simplifying
t = 15.280109889


Subproblem 2
t + -8 = -7.280109889

Simplifying
t + -8 = -7.280109889

Reorder the terms:
-8 + t = -7.280109889

Solving
-8 + t = -7.280109889

Solving for variable 't'.

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

Add '8' to each side of the equation.
-8 + 8 + t = -7.280109889 + 8

Combine like terms: -8 + 8 = 0
0 + t = -7.280109889 + 8
t = -7.280109889 + 8

Combine like terms: -7.280109889 + 8 = 0.719890111
t = 0.719890111

Simplifying
t = 0.719890111


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {15.280109889, 0.719890111}
Solution
t = {15.280109889, 0.719890111}

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