(7u^2+3u+1)-(8u^2-9u-6)+(-6u^2-6u+3)=

Solution for (7u^2+3u+1)-(8u^2-9u-6)+(-6u^2-6u+3)= equation:

Simplifying
(7u2 + 3u + 1) + -1(8u2 + -9u + -6) + (-6u2 + -6u + 3) = 0

Reorder the terms:
(1 + 3u + 7u2) + -1(8u2 + -9u + -6) + (-6u2 + -6u + 3) = 0

Remove parenthesis around (1 + 3u + 7u2)
1 + 3u + 7u2 + -1(8u2 + -9u + -6) + (-6u2 + -6u + 3) = 0

Reorder the terms:
1 + 3u + 7u2 + -1(-6 + -9u + 8u2) + (-6u2 + -6u + 3) = 0
1 + 3u + 7u2 + (-6 * -1 + -9u * -1 + 8u2 * -1) + (-6u2 + -6u + 3) = 0
1 + 3u + 7u2 + (6 + 9u + -8u2) + (-6u2 + -6u + 3) = 0

Reorder the terms:
1 + 3u + 7u2 + 6 + 9u + -8u2 + (3 + -6u + -6u2) = 0

Remove parenthesis around (3 + -6u + -6u2)
1 + 3u + 7u2 + 6 + 9u + -8u2 + 3 + -6u + -6u2 = 0

Reorder the terms:
1 + 6 + 3 + 3u + 9u + -6u + 7u2 + -8u2 + -6u2 = 0

Combine like terms: 1 + 6 = 7
7 + 3 + 3u + 9u + -6u + 7u2 + -8u2 + -6u2 = 0

Combine like terms: 7 + 3 = 10
10 + 3u + 9u + -6u + 7u2 + -8u2 + -6u2 = 0

Combine like terms: 3u + 9u = 12u
10 + 12u + -6u + 7u2 + -8u2 + -6u2 = 0

Combine like terms: 12u + -6u = 6u
10 + 6u + 7u2 + -8u2 + -6u2 = 0

Combine like terms: 7u2 + -8u2 = -1u2
10 + 6u + -1u2 + -6u2 = 0

Combine like terms: -1u2 + -6u2 = -7u2
10 + 6u + -7u2 = 0

Solving
10 + 6u + -7u2 = 0

Solving for variable 'u'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-1.428571429 + -0.8571428571u + u2 = 0

Move the constant term to the right:

Add '1.428571429' to each side of the equation.
-1.428571429 + -0.8571428571u + 1.428571429 + u2 = 0 + 1.428571429

Reorder the terms:
-1.428571429 + 1.428571429 + -0.8571428571u + u2 = 0 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + -0.8571428571u + u2 = 0 + 1.428571429
-0.8571428571u + u2 = 0 + 1.428571429

Combine like terms: 0 + 1.428571429 = 1.428571429
-0.8571428571u + u2 = 1.428571429

The u term is -0.8571428571u.  Take half its coefficient (-0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
-0.8571428571u + 0.1836734694 + u2 = 1.428571429 + 0.1836734694

Reorder the terms:
0.1836734694 + -0.8571428571u + u2 = 1.428571429 + 0.1836734694

Combine like terms: 1.428571429 + 0.1836734694 = 1.6122448984
0.1836734694 + -0.8571428571u + u2 = 1.6122448984

Factor a perfect square on the left side:
(u + -0.4285714286)(u + -0.4285714286) = 1.6122448984

Calculate the square root of the right side: 1.26974206

Break this problem into two subproblems by setting 
(u + -0.4285714286) equal to 1.26974206 and -1.26974206.

Subproblem 1
u + -0.4285714286 = 1.26974206

Simplifying
u + -0.4285714286 = 1.26974206

Reorder the terms:
-0.4285714286 + u = 1.26974206

Solving
-0.4285714286 + u = 1.26974206

Solving for variable 'u'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + u = 1.26974206 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + u = 1.26974206 + 0.4285714286
u = 1.26974206 + 0.4285714286

Combine like terms: 1.26974206 + 0.4285714286 = 1.6983134886
u = 1.6983134886

Simplifying
u = 1.6983134886

Subproblem 2
u + -0.4285714286 = -1.26974206

Simplifying
u + -0.4285714286 = -1.26974206

Reorder the terms:
-0.4285714286 + u = -1.26974206

Solving
-0.4285714286 + u = -1.26974206

Solving for variable 'u'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + u = -1.26974206 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + u = -1.26974206 + 0.4285714286
u = -1.26974206 + 0.4285714286

Combine like terms: -1.26974206 + 0.4285714286 = -0.8411706314
u = -0.8411706314

Simplifying
u = -0.8411706314

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.6983134886, -0.8411706314}