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

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


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

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

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

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

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

Reorder the terms:
(10wx + -7wx + -35w2 + 2x2) = 0

Combine like terms: 10wx + -7wx = 3wx
(3wx + -35w2 + 2x2) = 0

Solving
3wx + -35w2 + 2x2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-5w + -1x)(7w + -2x) = 0


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

Simplifying
-5w + -1x = 0

Solving
-5w + -1x = 0

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

Add 'x' to each side of the equation.
-5w + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-5w + 0 = 0 + x
-5w = 0 + x
Remove the zero:
-5w = x

Divide each side by '-5'.
w = -0.2x

Simplifying
w = -0.2x

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 = {-0.2x, 0.2857142857x}

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