78=x^2+6x+6

Solution for 78=x^2+6x+6 equation:

Simplifying
78 = x2 + 6x + 6

Reorder the terms:
78 = 6 + 6x + x2

Solving
78 = 6 + 6x + x2

Solving for variable 'x'.

Combine like terms: 78 + -6 = 72
72 + -6x + -1x2 = 6 + 6x + x2 + -6 + -6x + -1x2

Reorder the terms:
72 + -6x + -1x2 = 6 + -6 + 6x + -6x + x2 + -1x2

Combine like terms: 6 + -6 = 0
72 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2
72 + -6x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
72 + -6x + -1x2 = 0 + x2 + -1x2
72 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
72 + -6x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(12 + x) = 0

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

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {6, -12}