6X^2+78X=-240

Solution for 6X^2+78X=-240 equation:

Simplifying
6X2 + 78X = -240

Reorder the terms:
78X + 6X2 = -240

Solving
78X + 6X2 = -240

Solving for variable 'X'.

Reorder the terms:
240 + 78X + 6X2 = -240 + 240

Combine like terms: -240 + 240 = 0
240 + 78X + 6X2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(40 + 13X + X2) = 0

Factor a trinomial.
6((8 + X)(5 + X)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(8 + X)' equal to zero and attempt to solve:

Simplifying
8 + X = 0

Solving
8 + X = 0

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

Add '-8' to each side of the equation.
8 + -8 + X = 0 + -8

Combine like terms: 8 + -8 = 0
0 + X = 0 + -8
X = 0 + -8

Combine like terms: 0 + -8 = -8
X = -8

Simplifying
X = -8
Subproblem 2
Set the factor '(5 + X)' equal to zero and attempt to solve:

Simplifying
5 + X = 0

Solving
5 + X = 0

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

Add '-5' to each side of the equation.
5 + -5 + X = 0 + -5

Combine like terms: 5 + -5 = 0
0 + X = 0 + -5
X = 0 + -5

Combine like terms: 0 + -5 = -5
X = -5

Simplifying
X = -5
Solution
X = {-8, -5}