-6u^2+23u-16=0

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Solution for -6u^2+23u-16=0 equation: 


Simplifying
-6u2 + 23u + -16 = 0

Reorder the terms:
-16 + 23u + -6u2 = 0

Solving
-16 + 23u + -6u2 = 0

Solving for variable 'u'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
2.666666667 + -3.833333333u + u2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -3.833333333u + -2.666666667 + u2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -3.833333333u + u2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -3.833333333u + u2 = 0 + -2.666666667
-3.833333333u + u2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-3.833333333u + u2 = -2.666666667

The u term is -3.833333333u.  Take half its coefficient (-1.916666667).
Square it (3.673611112) and add it to both sides.

Add '3.673611112' to each side of the equation.
-3.833333333u + 3.673611112 + u2 = -2.666666667 + 3.673611112

Reorder the terms:
3.673611112 + -3.833333333u + u2 = -2.666666667 + 3.673611112

Combine like terms: -2.666666667 + 3.673611112 = 1.006944445
3.673611112 + -3.833333333u + u2 = 1.006944445

Factor a perfect square on the left side:
(u + -1.916666667)(u + -1.916666667) = 1.006944445

Calculate the square root of the right side: 1.003466215

Break this problem into two subproblems by setting 
(u + -1.916666667) equal to 1.003466215 and -1.003466215.


Subproblem 1
u + -1.916666667 = 1.003466215

Simplifying
u + -1.916666667 = 1.003466215

Reorder the terms:
-1.916666667 + u = 1.003466215

Solving
-1.916666667 + u = 1.003466215

Solving for variable 'u'.

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

Add '1.916666667' to each side of the equation.
-1.916666667 + 1.916666667 + u = 1.003466215 + 1.916666667

Combine like terms: -1.916666667 + 1.916666667 = 0.000000000
0.000000000 + u = 1.003466215 + 1.916666667
u = 1.003466215 + 1.916666667

Combine like terms: 1.003466215 + 1.916666667 = 2.920132882
u = 2.920132882

Simplifying
u = 2.920132882


Subproblem 2
u + -1.916666667 = -1.003466215

Simplifying
u + -1.916666667 = -1.003466215

Reorder the terms:
-1.916666667 + u = -1.003466215

Solving
-1.916666667 + u = -1.003466215

Solving for variable 'u'.

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

Add '1.916666667' to each side of the equation.
-1.916666667 + 1.916666667 + u = -1.003466215 + 1.916666667

Combine like terms: -1.916666667 + 1.916666667 = 0.000000000
0.000000000 + u = -1.003466215 + 1.916666667
u = -1.003466215 + 1.916666667

Combine like terms: -1.003466215 + 1.916666667 = 0.913200452
u = 0.913200452

Simplifying
u = 0.913200452


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {2.920132882, 0.913200452}

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