6x^2+54x+78=-6

Solution for 6x^2+54x+78=-6 equation:

Simplifying
6x2 + 54x + 78 = -6

Reorder the terms:
78 + 54x + 6x2 = -6

Solving
78 + 54x + 6x2 = -6

Solving for variable 'x'.

Reorder the terms:
78 + 6 + 54x + 6x2 = -6 + 6

Combine like terms: 78 + 6 = 84
84 + 54x + 6x2 = -6 + 6

Combine like terms: -6 + 6 = 0
84 + 54x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(14 + 9x + x2) = 0

Factor a trinomial.
6((7 + x)(2 + x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-7, -2}