u^2+2u+6u+12=0

Solution for u^2+2u+6u+12=0 equation:

Simplifying
u2 + 2u + 6u + 12 = 0

Reorder the terms:
12 + 2u + 6u + u2 = 0

Combine like terms: 2u + 6u = 8u
12 + 8u + u2 = 0

Solving
12 + 8u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6 + u)(2 + u) = 0

Subproblem 1
Set the factor '(6 + u)' equal to zero and attempt to solve:

Simplifying
6 + u = 0

Solving
6 + u = 0

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

Add '-6' to each side of the equation.
6 + -6 + u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + u = 0 + -6
u = 0 + -6

Combine like terms: 0 + -6 = -6
u = -6

Simplifying
u = -6
Subproblem 2
Set the factor '(2 + u)' equal to zero and attempt to solve:

Simplifying
2 + u = 0

Solving
2 + u = 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 + u = 0 + -2

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

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

Simplifying
u = -2
Solution
u = {-6, -2}