2w^2+3w-77=0

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Solution for 2w^2+3w-77=0 equation: 


Simplifying
2w2 + 3w + -77 = 0

Reorder the terms:
-77 + 3w + 2w2 = 0

Solving
-77 + 3w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + -1w)(11 + -2w) = 0


Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve:

Simplifying
-7 + -1w = 0

Solving
-7 + -1w = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1w = 0 + 7
-1w = 0 + 7

Combine like terms: 0 + 7 = 7
-1w = 7

Divide each side by '-1'.
w = -7

Simplifying
w = -7

Subproblem 2
Set the factor '(11 + -2w)' equal to zero and attempt to solve:

Simplifying
11 + -2w = 0

Solving
11 + -2w = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2w = 0 + -11
-2w = 0 + -11

Combine like terms: 0 + -11 = -11
-2w = -11

Divide each side by '-2'.
w = 5.5

Simplifying
w = 5.5
Solution
w = {-7, 5.5}

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