(2w-5)(w+7)=0

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Solution for (2w-5)(w+7)=0 equation: 


Simplifying
(2w + -5)(w + 7) = 0

Reorder the terms:
(-5 + 2w)(w + 7) = 0

Reorder the terms:
(-5 + 2w)(7 + w) = 0

Multiply (-5 + 2w) * (7 + w)
(-5(7 + w) + 2w * (7 + w)) = 0
((7 * -5 + w * -5) + 2w * (7 + w)) = 0
((-35 + -5w) + 2w * (7 + w)) = 0
(-35 + -5w + (7 * 2w + w * 2w)) = 0
(-35 + -5w + (14w + 2w2)) = 0

Combine like terms: -5w + 14w = 9w
(-35 + 9w + 2w2) = 0

Solving
-35 + 9w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + -1w)(5 + -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 '(5 + -2w)' equal to zero and attempt to solve:

Simplifying
5 + -2w = 0

Solving
5 + -2w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2w = 0 + -5
-2w = 0 + -5

Combine like terms: 0 + -5 = -5
-2w = -5

Divide each side by '-2'.
w = 2.5

Simplifying
w = 2.5
Solution
w = {-7, 2.5}

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