(x*x)+(7*x)=-12

Solution for (x*x)+(7*x)=-12 equation:

Simplifying
(x * x) + (7x) = -12

Multiply x * x
(x2) + (7x) = -12
x2 + (7x) = -12

Reorder the terms:
(7x) + x2 = -12

Solving
(7x) + x2 = -12

Solving for variable 'x'.

Reorder the terms:
12 + (7x) + x2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + (7x) + x2 = 0

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

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

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

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