(8w+17)(11w-23)=0

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Solution for (8w+17)(11w-23)=0 equation: 


Simplifying
(8w + 17)(11w + -23) = 0

Reorder the terms:
(17 + 8w)(11w + -23) = 0

Reorder the terms:
(17 + 8w)(-23 + 11w) = 0

Multiply (17 + 8w) * (-23 + 11w)
(17(-23 + 11w) + 8w * (-23 + 11w)) = 0
((-23 * 17 + 11w * 17) + 8w * (-23 + 11w)) = 0
((-391 + 187w) + 8w * (-23 + 11w)) = 0
(-391 + 187w + (-23 * 8w + 11w * 8w)) = 0
(-391 + 187w + (-184w + 88w2)) = 0

Combine like terms: 187w + -184w = 3w
(-391 + 3w + 88w2) = 0

Solving
-391 + 3w + 88w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-17 + -8w)(23 + -11w) = 0


Subproblem 1
Set the factor '(-17 + -8w)' equal to zero and attempt to solve:

Simplifying
-17 + -8w = 0

Solving
-17 + -8w = 0

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

Add '17' to each side of the equation.
-17 + 17 + -8w = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -8w = 0 + 17
-8w = 0 + 17

Combine like terms: 0 + 17 = 17
-8w = 17

Divide each side by '-8'.
w = -2.125

Simplifying
w = -2.125

Subproblem 2
Set the factor '(23 + -11w)' equal to zero and attempt to solve:

Simplifying
23 + -11w = 0

Solving
23 + -11w = 0

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

Add '-23' to each side of the equation.
23 + -23 + -11w = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -11w = 0 + -23
-11w = 0 + -23

Combine like terms: 0 + -23 = -23
-11w = -23

Divide each side by '-11'.
w = 2.090909091

Simplifying
w = 2.090909091
Solution
w = {-2.125, 2.090909091}

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