-2u(5u-7)+6u=2(u+3)

Solution for -2u(5u-7)+6u=2(u+3) equation:

Simplifying
-2u(5u + -7) + 6u = 2(u + 3)

Reorder the terms:
-2u(-7 + 5u) + 6u = 2(u + 3)
(-7 * -2u + 5u * -2u) + 6u = 2(u + 3)
(14u + -10u2) + 6u = 2(u + 3)

Reorder the terms:
14u + 6u + -10u2 = 2(u + 3)

Combine like terms: 14u + 6u = 20u
20u + -10u2 = 2(u + 3)

Reorder the terms:
20u + -10u2 = 2(3 + u)
20u + -10u2 = (3 * 2 + u * 2)
20u + -10u2 = (6 + 2u)

Solving
20u + -10u2 = 6 + 2u

Solving for variable 'u'.

Reorder the terms:
-6 + 20u + -2u + -10u2 = 6 + 2u + -6 + -2u

Combine like terms: 20u + -2u = 18u
-6 + 18u + -10u2 = 6 + 2u + -6 + -2u

Reorder the terms:
-6 + 18u + -10u2 = 6 + -6 + 2u + -2u

Combine like terms: 6 + -6 = 0
-6 + 18u + -10u2 = 0 + 2u + -2u
-6 + 18u + -10u2 = 2u + -2u

Combine like terms: 2u + -2u = 0
-6 + 18u + -10u2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 9u + -5u2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 9u + -5u2)' equal to zero and attempt to solve:

Simplifying
-3 + 9u + -5u2 = 0

Solving
-3 + 9u + -5u2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.6 + -1.8u + u2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -1.8u + -0.6 + u2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -1.8u + u2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -1.8u + u2 = 0 + -0.6
-1.8u + u2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-1.8u + u2 = -0.6

The u term is -1.8u.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8u + 0.81 + u2 = -0.6 + 0.81

Reorder the terms:
0.81 + -1.8u + u2 = -0.6 + 0.81

Combine like terms: -0.6 + 0.81 = 0.21
0.81 + -1.8u + u2 = 0.21

Factor a perfect square on the left side:
(u + -0.9)(u + -0.9) = 0.21

Calculate the square root of the right side: 0.458257569

Break this problem into two subproblems by setting 
(u + -0.9) equal to 0.458257569 and -0.458257569.

Subproblem 1
u + -0.9 = 0.458257569

Simplifying
u + -0.9 = 0.458257569

Reorder the terms:
-0.9 + u = 0.458257569

Solving
-0.9 + u = 0.458257569

Solving for variable 'u'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + u = 0.458257569 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + u = 0.458257569 + 0.9
u = 0.458257569 + 0.9

Combine like terms: 0.458257569 + 0.9 = 1.358257569
u = 1.358257569

Simplifying
u = 1.358257569

Subproblem 2
u + -0.9 = -0.458257569

Simplifying
u + -0.9 = -0.458257569

Reorder the terms:
-0.9 + u = -0.458257569

Solving
-0.9 + u = -0.458257569

Solving for variable 'u'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + u = -0.458257569 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + u = -0.458257569 + 0.9
u = -0.458257569 + 0.9

Combine like terms: -0.458257569 + 0.9 = 0.441742431
u = 0.441742431

Simplifying
u = 0.441742431

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.358257569, 0.441742431}
Solution
u = {1.358257569, 0.441742431}