36w^2-77w-9=0

Solution for 36w^2-77w-9=0 equation:

Simplifying
36w2 + -77w + -9 = 0

Reorder the terms:
-9 + -77w + 36w2 = 0

Solving
-9 + -77w + 36w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -9w)(9 + -4w) = 0

Subproblem 1
Set the factor '(-1 + -9w)' equal to zero and attempt to solve:

Simplifying
-1 + -9w = 0

Solving
-1 + -9w = 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 + -9w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -9w = 0 + 1
-9w = 0 + 1

Combine like terms: 0 + 1 = 1
-9w = 1

Divide each side by '-9'.
w = -0.1111111111

Simplifying
w = -0.1111111111
Subproblem 2
Set the factor '(9 + -4w)' equal to zero and attempt to solve:

Simplifying
9 + -4w = 0

Solving
9 + -4w = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4w = 0 + -9
-4w = 0 + -9

Combine like terms: 0 + -9 = -9
-4w = -9

Divide each side by '-4'.
w = 2.25

Simplifying
w = 2.25
Solution
w = {-0.1111111111, 2.25}