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

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


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

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

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

Multiply (-5w + 2x) * (-7w + 2x)
(-5w * (-7w + 2x) + 2x * (-7w + 2x)) = 0
((-7w * -5w + 2x * -5w) + 2x * (-7w + 2x)) = 0

Reorder the terms:
((-10wx + 35w2) + 2x * (-7w + 2x)) = 0
((-10wx + 35w2) + 2x * (-7w + 2x)) = 0
(-10wx + 35w2 + (-7w * 2x + 2x * 2x)) = 0
(-10wx + 35w2 + (-14wx + 4x2)) = 0

Reorder the terms:
(-10wx + -14wx + 35w2 + 4x2) = 0

Combine like terms: -10wx + -14wx = -24wx
(-24wx + 35w2 + 4x2) = 0

Solving
-24wx + 35w2 + 4x2 = 0

Solving for variable 'w'.

Factor a trinomial.
(5w + -2x)(7w + -2x) = 0


Subproblem 1
Set the factor '(5w + -2x)' equal to zero and attempt to solve:

Simplifying
5w + -2x = 0

Solving
5w + -2x = 0

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

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

Combine like terms: -2x + 2x = 0
5w + 0 = 0 + 2x
5w = 0 + 2x
Remove the zero:
5w = 2x

Divide each side by '5'.
w = 0.4x

Simplifying
w = 0.4x

Subproblem 2
Set the factor '(7w + -2x)' equal to zero and attempt to solve:

Simplifying
7w + -2x = 0

Solving
7w + -2x = 0

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

Add '2x' to each side of the equation.
7w + -2x + 2x = 0 + 2x

Combine like terms: -2x + 2x = 0
7w + 0 = 0 + 2x
7w = 0 + 2x
Remove the zero:
7w = 2x

Divide each side by '7'.
w = 0.2857142857x

Simplifying
w = 0.2857142857x
Solution
w = {0.4x, 0.2857142857x}

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