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

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

Simplifying
u2 + 6 + u + 6u = 0

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

Combine like terms: u + 6u = 7u
6 + 7u + u2 = 0

Solving
6 + 7u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6 + u)(1 + 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 '(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
Solution
u = {-6, -1}