6=(x^2+7x+12)

Solution for 6=(x^2+7x+12) equation:

Simplifying
6 = (x2 + 7x + 12)

Reorder the terms:
6 = (12 + 7x + x2)

Remove parenthesis around (12 + 7x + x2)
6 = 12 + 7x + x2

Solving
6 = 12 + 7x + x2

Solving for variable 'x'.

Combine like terms: 6 + -12 = -6
-6 + -7x + -1x2 = 12 + 7x + x2 + -12 + -7x + -1x2

Reorder the terms:
-6 + -7x + -1x2 = 12 + -12 + 7x + -7x + x2 + -1x2

Combine like terms: 12 + -12 = 0
-6 + -7x + -1x2 = 0 + 7x + -7x + x2 + -1x2
-6 + -7x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
-6 + -7x + -1x2 = 0 + x2 + -1x2
-6 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + -7x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 7x + x2) = 0

Factor a trinomial.
-1((6 + x)(1 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

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

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

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

Simplifying
x = -6
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-6, -1}