j^2+7j+12=0

Solution for j^2+7j+12=0 equation:

Simplifying
j2 + 7j + 12 = 0

Reorder the terms:
12 + 7j + j2 = 0

Solving
12 + 7j + j2 = 0

Solving for variable 'j'.

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

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

Simplifying
4 + j = 0

Solving
4 + j = 0

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

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

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

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

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

Simplifying
3 + j = 0

Solving
3 + j = 0

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

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

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

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

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