-3u^2+42u-57=0

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Solution for -3u^2+42u-57=0 equation: 


Simplifying
-3u2 + 42u + -57 = 0

Reorder the terms:
-57 + 42u + -3u2 = 0

Solving
-57 + 42u + -3u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-19 + 14u + -1u2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-19 + 14u + -1u2)' equal to zero and attempt to solve:

Simplifying
-19 + 14u + -1u2 = 0

Solving
-19 + 14u + -1u2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
19 + -14u + u2 = 0

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + -14u + -19 + u2 = 0 + -19

Reorder the terms:
19 + -19 + -14u + u2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -14u + u2 = 0 + -19
-14u + u2 = 0 + -19

Combine like terms: 0 + -19 = -19
-14u + u2 = -19

The u term is -14u.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14u + 49 + u2 = -19 + 49

Reorder the terms:
49 + -14u + u2 = -19 + 49

Combine like terms: -19 + 49 = 30
49 + -14u + u2 = 30

Factor a perfect square on the left side:
(u + -7)(u + -7) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(u + -7) equal to 5.477225575 and -5.477225575.


Subproblem 1
u + -7 = 5.477225575

Simplifying
u + -7 = 5.477225575

Reorder the terms:
-7 + u = 5.477225575

Solving
-7 + u = 5.477225575

Solving for variable 'u'.

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

Add '7' to each side of the equation.
-7 + 7 + u = 5.477225575 + 7

Combine like terms: -7 + 7 = 0
0 + u = 5.477225575 + 7
u = 5.477225575 + 7

Combine like terms: 5.477225575 + 7 = 12.477225575
u = 12.477225575

Simplifying
u = 12.477225575


Subproblem 2
u + -7 = -5.477225575

Simplifying
u + -7 = -5.477225575

Reorder the terms:
-7 + u = -5.477225575

Solving
-7 + u = -5.477225575

Solving for variable 'u'.

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

Add '7' to each side of the equation.
-7 + 7 + u = -5.477225575 + 7

Combine like terms: -7 + 7 = 0
0 + u = -5.477225575 + 7
u = -5.477225575 + 7

Combine like terms: -5.477225575 + 7 = 1.522774425
u = 1.522774425

Simplifying
u = 1.522774425


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {12.477225575, 1.522774425}
Solution
u = {12.477225575, 1.522774425}

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