6w^2-72w-78=0

Solution for 6w^2-72w-78=0 equation:

Simplifying
6w2 + -72w + -78 = 0

Reorder the terms:
-78 + -72w + 6w2 = 0

Solving
-78 + -72w + 6w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-13 + -12w + w2) = 0

Factor a trinomial.
6((-1 + -1w)(13 + -1w)) = 0

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

Simplifying
-1 + -1w = 0

Solving
-1 + -1w = 0

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

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

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

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

Divide each side by '-1'.
w = -1

Simplifying
w = -1
Subproblem 2
Set the factor '(13 + -1w)' equal to zero and attempt to solve:

Simplifying
13 + -1w = 0

Solving
13 + -1w = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1w = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1w = 0 + -13
-1w = 0 + -13

Combine like terms: 0 + -13 = -13
-1w = -13

Divide each side by '-1'.
w = 13

Simplifying
w = 13
Solution
w = {-1, 13}