(u^2)+7u+12=0

Solution for (u^2)+7u+12=0 equation:

Simplifying
(u2) + 7u + 12 = 0
u2 + 7u + 12 = 0

Reorder the terms:
12 + 7u + u2 = 0

Solving
12 + 7u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(4 + u)(3 + u) = 0

Subproblem 1
Set the factor '(4 + u)' equal to zero and attempt to solve:

Simplifying
4 + u = 0

Solving
4 + u = 0

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

Add '-4' to each side of the equation.
4 + -4 + u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + u = 0 + -4
u = 0 + -4

Combine like terms: 0 + -4 = -4
u = -4

Simplifying
u = -4
Subproblem 2
Set the factor '(3 + u)' equal to zero and attempt to solve:

Simplifying
3 + u = 0

Solving
3 + u = 0

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

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

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

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

Simplifying
u = -3
Solution
u = {-4, -3}