10u^2+24u+12=0

Solution for 10u^2+24u+12=0 equation:

Simplifying
10u2 + 24u + 12 = 0

Reorder the terms:
12 + 24u + 10u2 = 0

Solving
12 + 24u + 10u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 12u + 5u2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 12u + 5u2)' equal to zero and attempt to solve:

Simplifying
6 + 12u + 5u2 = 0

Solving
6 + 12u + 5u2 = 0

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

Divide each side by '5'.
1.2 + 2.4u + u2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 2.4u + -1.2 + u2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 2.4u + u2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 2.4u + u2 = 0 + -1.2
2.4u + u2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
2.4u + u2 = -1.2

The u term is 2.4u.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4u + 1.44 + u2 = -1.2 + 1.44

Reorder the terms:
1.44 + 2.4u + u2 = -1.2 + 1.44

Combine like terms: -1.2 + 1.44 = 0.24
1.44 + 2.4u + u2 = 0.24

Factor a perfect square on the left side:
(u + 1.2)(u + 1.2) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(u + 1.2) equal to 0.489897949 and -0.489897949.

Subproblem 1
u + 1.2 = 0.489897949

Simplifying
u + 1.2 = 0.489897949

Reorder the terms:
1.2 + u = 0.489897949

Solving
1.2 + u = 0.489897949

Solving for variable 'u'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + u = 0.489897949 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + u = 0.489897949 + -1.2
u = 0.489897949 + -1.2

Combine like terms: 0.489897949 + -1.2 = -0.710102051
u = -0.710102051

Simplifying
u = -0.710102051

Subproblem 2
u + 1.2 = -0.489897949

Simplifying
u + 1.2 = -0.489897949

Reorder the terms:
1.2 + u = -0.489897949

Solving
1.2 + u = -0.489897949

Solving for variable 'u'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + u = -0.489897949 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + u = -0.489897949 + -1.2
u = -0.489897949 + -1.2

Combine like terms: -0.489897949 + -1.2 = -1.689897949
u = -1.689897949

Simplifying
u = -1.689897949

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-0.710102051, -1.689897949}
Solution
u = {-0.710102051, -1.689897949}