4u-5+3(2u+1)=-2u(u+4)

Solution for 4u-5+3(2u+1)=-2u(u+4) equation:

Simplifying
4u + -5 + 3(2u + 1) = -2u(u + 4)

Reorder the terms:
4u + -5 + 3(1 + 2u) = -2u(u + 4)
4u + -5 + (1 * 3 + 2u * 3) = -2u(u + 4)
4u + -5 + (3 + 6u) = -2u(u + 4)

Reorder the terms:
-5 + 3 + 4u + 6u = -2u(u + 4)

Combine like terms: -5 + 3 = -2
-2 + 4u + 6u = -2u(u + 4)

Combine like terms: 4u + 6u = 10u
-2 + 10u = -2u(u + 4)

Reorder the terms:
-2 + 10u = -2u(4 + u)
-2 + 10u = (4 * -2u + u * -2u)
-2 + 10u = (-8u + -2u2)

Solving
-2 + 10u = -8u + -2u2

Solving for variable 'u'.

Combine like terms: 10u + 8u = 18u
-2 + 18u + 2u2 = -8u + -2u2 + 8u + 2u2

Reorder the terms:
-2 + 18u + 2u2 = -8u + 8u + -2u2 + 2u2

Combine like terms: -8u + 8u = 0
-2 + 18u + 2u2 = 0 + -2u2 + 2u2
-2 + 18u + 2u2 = -2u2 + 2u2

Combine like terms: -2u2 + 2u2 = 0
-2 + 18u + 2u2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 9u + u2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 9u + u2)' equal to zero and attempt to solve:

Simplifying
-1 + 9u + u2 = 0

Solving
-1 + 9u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 9u + 1 + u2 = 0 + 1

Reorder the terms:
-1 + 1 + 9u + u2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 9u + u2 = 0 + 1
9u + u2 = 0 + 1

Combine like terms: 0 + 1 = 1
9u + u2 = 1

The u term is 9u.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9u + 20.25 + u2 = 1 + 20.25

Reorder the terms:
20.25 + 9u + u2 = 1 + 20.25

Combine like terms: 1 + 20.25 = 21.25
20.25 + 9u + u2 = 21.25

Factor a perfect square on the left side:
(u + 4.5)(u + 4.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(u + 4.5) equal to 4.609772229 and -4.609772229.

Subproblem 1
u + 4.5 = 4.609772229

Simplifying
u + 4.5 = 4.609772229

Reorder the terms:
4.5 + u = 4.609772229

Solving
4.5 + u = 4.609772229

Solving for variable 'u'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + u = 4.609772229 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + u = 4.609772229 + -4.5
u = 4.609772229 + -4.5

Combine like terms: 4.609772229 + -4.5 = 0.109772229
u = 0.109772229

Simplifying
u = 0.109772229

Subproblem 2
u + 4.5 = -4.609772229

Simplifying
u + 4.5 = -4.609772229

Reorder the terms:
4.5 + u = -4.609772229

Solving
4.5 + u = -4.609772229

Solving for variable 'u'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + u = -4.609772229 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + u = -4.609772229 + -4.5
u = -4.609772229 + -4.5

Combine like terms: -4.609772229 + -4.5 = -9.109772229
u = -9.109772229

Simplifying
u = -9.109772229

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.109772229, -9.109772229}
Solution
u = {0.109772229, -9.109772229}