30u^2+30u-6=0

Solution for 30u^2+30u-6=0 equation:

Simplifying
30u2 + 30u + -6 = 0

Reorder the terms:
-6 + 30u + 30u2 = 0

Solving
-6 + 30u + 30u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 5u + 5u2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + 5u + 5u2)' equal to zero and attempt to solve:

Simplifying
-1 + 5u + 5u2 = 0

Solving
-1 + 5u + 5u2 = 0

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

Divide each side by '5'.
-0.2 + u + u2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + u + 0.2 + u2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + u + u2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + u + u2 = 0 + 0.2
u + u2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
u + u2 = 0.2

The u term is u.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + u2 = 0.2 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + u2 = 0.2 + 0.25

Combine like terms: 0.2 + 0.25 = 0.45
1.25 + u2 = 0.45

Factor a perfect square on the left side:
(u + 0.5)(u + 0.5) = 0.45

Calculate the square root of the right side: 0.670820393

Break this problem into two subproblems by setting 
(u + 0.5) equal to 0.670820393 and -0.670820393.

Subproblem 1
u + 0.5 = 0.670820393

Simplifying
u + 0.5 = 0.670820393

Reorder the terms:
0.5 + u = 0.670820393

Solving
0.5 + u = 0.670820393

Solving for variable 'u'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = 0.670820393 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = 0.670820393 + -0.5
u = 0.670820393 + -0.5

Combine like terms: 0.670820393 + -0.5 = 0.170820393
u = 0.170820393

Simplifying
u = 0.170820393

Subproblem 2
u + 0.5 = -0.670820393

Simplifying
u + 0.5 = -0.670820393

Reorder the terms:
0.5 + u = -0.670820393

Solving
0.5 + u = -0.670820393

Solving for variable 'u'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = -0.670820393 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = -0.670820393 + -0.5
u = -0.670820393 + -0.5

Combine like terms: -0.670820393 + -0.5 = -1.170820393
u = -1.170820393

Simplifying
u = -1.170820393

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.170820393, -1.170820393}
Solution
u = {0.170820393, -1.170820393}