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

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


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

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

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

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

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

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

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

Solving
-25wx + -25w2 + 24x2 = 0

Solving for variable 'w'.

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


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

Simplifying
-5w + -8x = 0

Solving
-5w + -8x = 0

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

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

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

Divide each side by '-5'.
w = -1.6x

Simplifying
w = -1.6x

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 = {-1.6x, 0.6x}

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