6u^2+10u+4=0

Solution for 6u^2+10u+4=0 equation:

Simplifying
6u2 + 10u + 4 = 0

Reorder the terms:
4 + 10u + 6u2 = 0

Solving
4 + 10u + 6u2 = 0

Solving for variable 'u'.

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

Factor a trinomial.
2((1 + u)(2 + 3u)) = 0

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

Simplifying
1 + u = 0

Solving
1 + u = 0

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

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

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

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

Simplifying
u = -1
Subproblem 2
Set the factor '(2 + 3u)' equal to zero and attempt to solve:

Simplifying
2 + 3u = 0

Solving
2 + 3u = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3u = 0 + -2
3u = 0 + -2

Combine like terms: 0 + -2 = -2
3u = -2

Divide each side by '3'.
u = -0.6666666667

Simplifying
u = -0.6666666667
Solution
u = {-1, -0.6666666667}