27w^2+54w-9720=0

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Solution for 27w^2+54w-9720=0 equation: 


Simplifying
27w2 + 54w + -9720 = 0

Reorder the terms:
-9720 + 54w + 27w2 = 0

Solving
-9720 + 54w + 27w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '27'.
27(-360 + 2w + w2) = 0

Factor a trinomial.
27((-20 + -1w)(18 + -1w)) = 0

Ignore the factor 27.

Subproblem 1
Set the factor '(-20 + -1w)' equal to zero and attempt to solve:

Simplifying
-20 + -1w = 0

Solving
-20 + -1w = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1w = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1w = 0 + 20
-1w = 0 + 20

Combine like terms: 0 + 20 = 20
-1w = 20

Divide each side by '-1'.
w = -20

Simplifying
w = -20

Subproblem 2
Set the factor '(18 + -1w)' equal to zero and attempt to solve:

Simplifying
18 + -1w = 0

Solving
18 + -1w = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1w = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1w = 0 + -18
-1w = 0 + -18

Combine like terms: 0 + -18 = -18
-1w = -18

Divide each side by '-1'.
w = 18

Simplifying
w = 18
Solution
w = {-20, 18}

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