-2u(2u-5)+6u=-4(u+1)

Solution for -2u(2u-5)+6u=-4(u+1) equation:

Simplifying
-2u(2u + -5) + 6u = -4(u + 1)

Reorder the terms:
-2u(-5 + 2u) + 6u = -4(u + 1)
(-5 * -2u + 2u * -2u) + 6u = -4(u + 1)
(10u + -4u2) + 6u = -4(u + 1)

Reorder the terms:
10u + 6u + -4u2 = -4(u + 1)

Combine like terms: 10u + 6u = 16u
16u + -4u2 = -4(u + 1)

Reorder the terms:
16u + -4u2 = -4(1 + u)
16u + -4u2 = (1 * -4 + u * -4)
16u + -4u2 = (-4 + -4u)

Solving
16u + -4u2 = -4 + -4u

Solving for variable 'u'.

Reorder the terms:
4 + 16u + 4u + -4u2 = -4 + -4u + 4 + 4u

Combine like terms: 16u + 4u = 20u
4 + 20u + -4u2 = -4 + -4u + 4 + 4u

Reorder the terms:
4 + 20u + -4u2 = -4 + 4 + -4u + 4u

Combine like terms: -4 + 4 = 0
4 + 20u + -4u2 = 0 + -4u + 4u
4 + 20u + -4u2 = -4u + 4u

Combine like terms: -4u + 4u = 0
4 + 20u + -4u2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 5u + -1u2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + 5u + -1u2)' equal to zero and attempt to solve:

Simplifying
1 + 5u + -1u2 = 0

Solving
1 + 5u + -1u2 = 0

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

Divide each side by '-1'.
-1 + -5u + u2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -5u + 1 + u2 = 0 + 1

Reorder the terms:
-1 + 1 + -5u + u2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5u + u2 = 0 + 1
-5u + u2 = 0 + 1

Combine like terms: 0 + 1 = 1
-5u + u2 = 1

The u term is -5u.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5u + 6.25 + u2 = 1 + 6.25

Reorder the terms:
6.25 + -5u + u2 = 1 + 6.25

Combine like terms: 1 + 6.25 = 7.25
6.25 + -5u + u2 = 7.25

Factor a perfect square on the left side:
(u + -2.5)(u + -2.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(u + -2.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
u + -2.5 = 2.692582404

Simplifying
u + -2.5 = 2.692582404

Reorder the terms:
-2.5 + u = 2.692582404

Solving
-2.5 + u = 2.692582404

Solving for variable 'u'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + u = 2.692582404 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + u = 2.692582404 + 2.5
u = 2.692582404 + 2.5

Combine like terms: 2.692582404 + 2.5 = 5.192582404
u = 5.192582404

Simplifying
u = 5.192582404

Subproblem 2
u + -2.5 = -2.692582404

Simplifying
u + -2.5 = -2.692582404

Reorder the terms:
-2.5 + u = -2.692582404

Solving
-2.5 + u = -2.692582404

Solving for variable 'u'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + u = -2.692582404 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + u = -2.692582404 + 2.5
u = -2.692582404 + 2.5

Combine like terms: -2.692582404 + 2.5 = -0.192582404
u = -0.192582404

Simplifying
u = -0.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {5.192582404, -0.192582404}
Solution
u = {5.192582404, -0.192582404}