(3x-5w)(5x+8w)=0

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Solution for (3x-5w)(5x+8w)=0 equation: 


Simplifying
(3x + -5w)(5x + 8w) = 0

Reorder the terms:
(-5w + 3x)(5x + 8w) = 0

Reorder the terms:
(-5w + 3x)(8w + 5x) = 0

Multiply (-5w + 3x) * (8w + 5x)
(-5w * (8w + 5x) + 3x * (8w + 5x)) = 0
((8w * -5w + 5x * -5w) + 3x * (8w + 5x)) = 0

Reorder the terms:
((-25wx + -40w2) + 3x * (8w + 5x)) = 0
((-25wx + -40w2) + 3x * (8w + 5x)) = 0
(-25wx + -40w2 + (8w * 3x + 5x * 3x)) = 0
(-25wx + -40w2 + (24wx + 15x2)) = 0

Reorder the terms:
(-25wx + 24wx + -40w2 + 15x2) = 0

Combine like terms: -25wx + 24wx = -1wx
(-1wx + -40w2 + 15x2) = 0

Solving
-1wx + -40w2 + 15x2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-8w + -5x)(5w + -3x) = 0


Subproblem 1
Set the factor '(-8w + -5x)' equal to zero and attempt to solve:

Simplifying
-8w + -5x = 0

Solving
-8w + -5x = 0

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

Add '5x' to each side of the equation.
-8w + -5x + 5x = 0 + 5x

Combine like terms: -5x + 5x = 0
-8w + 0 = 0 + 5x
-8w = 0 + 5x
Remove the zero:
-8w = 5x

Divide each side by '-8'.
w = -0.625x

Simplifying
w = -0.625x

Subproblem 2
Set the factor '(5w + -3x)' equal to zero and attempt to solve:

Simplifying
5w + -3x = 0

Solving
5w + -3x = 0

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

Add '3x' to each side of the equation.
5w + -3x + 3x = 0 + 3x

Combine like terms: -3x + 3x = 0
5w + 0 = 0 + 3x
5w = 0 + 3x
Remove the zero:
5w = 3x

Divide each side by '5'.
w = 0.6x

Simplifying
w = 0.6x
Solution
w = {-0.625x, 0.6x}

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