(2u^2+4u-7)+(8u^2-2u-9)-(-2u^2+4u+1)=0

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Solution for (2u^2+4u-7)+(8u^2-2u-9)-(-2u^2+4u+1)=0 equation: 


Simplifying
(2u2 + 4u + -7) + (8u2 + -2u + -9) + -1(-2u2 + 4u + 1) = 0

Reorder the terms:
(-7 + 4u + 2u2) + (8u2 + -2u + -9) + -1(-2u2 + 4u + 1) = 0

Remove parenthesis around (-7 + 4u + 2u2)
-7 + 4u + 2u2 + (8u2 + -2u + -9) + -1(-2u2 + 4u + 1) = 0

Reorder the terms:
-7 + 4u + 2u2 + (-9 + -2u + 8u2) + -1(-2u2 + 4u + 1) = 0

Remove parenthesis around (-9 + -2u + 8u2)
-7 + 4u + 2u2 + -9 + -2u + 8u2 + -1(-2u2 + 4u + 1) = 0

Reorder the terms:
-7 + 4u + 2u2 + -9 + -2u + 8u2 + -1(1 + 4u + -2u2) = 0
-7 + 4u + 2u2 + -9 + -2u + 8u2 + (1 * -1 + 4u * -1 + -2u2 * -1) = 0
-7 + 4u + 2u2 + -9 + -2u + 8u2 + (-1 + -4u + 2u2) = 0

Reorder the terms:
-7 + -9 + -1 + 4u + -2u + -4u + 2u2 + 8u2 + 2u2 = 0

Combine like terms: -7 + -9 = -16
-16 + -1 + 4u + -2u + -4u + 2u2 + 8u2 + 2u2 = 0

Combine like terms: -16 + -1 = -17
-17 + 4u + -2u + -4u + 2u2 + 8u2 + 2u2 = 0

Combine like terms: 4u + -2u = 2u
-17 + 2u + -4u + 2u2 + 8u2 + 2u2 = 0

Combine like terms: 2u + -4u = -2u
-17 + -2u + 2u2 + 8u2 + 2u2 = 0

Combine like terms: 2u2 + 8u2 = 10u2
-17 + -2u + 10u2 + 2u2 = 0

Combine like terms: 10u2 + 2u2 = 12u2
-17 + -2u + 12u2 = 0

Solving
-17 + -2u + 12u2 = 0

Solving for variable 'u'.

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

Divide each side by '12'.
-1.416666667 + -0.1666666667u + u2 = 0

Move the constant term to the right:

Add '1.416666667' to each side of the equation.
-1.416666667 + -0.1666666667u + 1.416666667 + u2 = 0 + 1.416666667

Reorder the terms:
-1.416666667 + 1.416666667 + -0.1666666667u + u2 = 0 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + -0.1666666667u + u2 = 0 + 1.416666667
-0.1666666667u + u2 = 0 + 1.416666667

Combine like terms: 0 + 1.416666667 = 1.416666667
-0.1666666667u + u2 = 1.416666667

The u term is -0.1666666667u.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667u + 0.006944444447 + u2 = 1.416666667 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667u + u2 = 1.416666667 + 0.006944444447

Combine like terms: 1.416666667 + 0.006944444447 = 1.423611111447
0.006944444447 + -0.1666666667u + u2 = 1.423611111447

Factor a perfect square on the left side:
(u + -0.08333333335)(u + -0.08333333335) = 1.423611111447

Calculate the square root of the right side: 1.193151755

Break this problem into two subproblems by setting 
(u + -0.08333333335) equal to 1.193151755 and -1.193151755.


Subproblem 1
u + -0.08333333335 = 1.193151755

Simplifying
u + -0.08333333335 = 1.193151755

Reorder the terms:
-0.08333333335 + u = 1.193151755

Solving
-0.08333333335 + u = 1.193151755

Solving for variable 'u'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + u = 1.193151755 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + u = 1.193151755 + 0.08333333335
u = 1.193151755 + 0.08333333335

Combine like terms: 1.193151755 + 0.08333333335 = 1.27648508835
u = 1.27648508835

Simplifying
u = 1.27648508835


Subproblem 2
u + -0.08333333335 = -1.193151755

Simplifying
u + -0.08333333335 = -1.193151755

Reorder the terms:
-0.08333333335 + u = -1.193151755

Solving
-0.08333333335 + u = -1.193151755

Solving for variable 'u'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + u = -1.193151755 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + u = -1.193151755 + 0.08333333335
u = -1.193151755 + 0.08333333335

Combine like terms: -1.193151755 + 0.08333333335 = -1.10981842165
u = -1.10981842165

Simplifying
u = -1.10981842165


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.27648508835, -1.10981842165}

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