(3x+2w)(8x-3w)=0

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Solution for (3x+2w)(8x-3w)=0 equation: 


Simplifying
(3x + 2w)(8x + -3w) = 0

Reorder the terms:
(2w + 3x)(8x + -3w) = 0

Reorder the terms:
(2w + 3x)(-3w + 8x) = 0

Multiply (2w + 3x) * (-3w + 8x)
(2w * (-3w + 8x) + 3x * (-3w + 8x)) = 0
((-3w * 2w + 8x * 2w) + 3x * (-3w + 8x)) = 0

Reorder the terms:
((16wx + -6w2) + 3x * (-3w + 8x)) = 0
((16wx + -6w2) + 3x * (-3w + 8x)) = 0
(16wx + -6w2 + (-3w * 3x + 8x * 3x)) = 0
(16wx + -6w2 + (-9wx + 24x2)) = 0

Reorder the terms:
(16wx + -9wx + -6w2 + 24x2) = 0

Combine like terms: 16wx + -9wx = 7wx
(7wx + -6w2 + 24x2) = 0

Solving
7wx + -6w2 + 24x2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-2w + -3x)(3w + -8x) = 0


Subproblem 1
Set the factor '(-2w + -3x)' equal to zero and attempt to solve:

Simplifying
-2w + -3x = 0

Solving
-2w + -3x = 0

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

Add '3x' to each side of the equation.
-2w + -3x + 3x = 0 + 3x

Combine like terms: -3x + 3x = 0
-2w + 0 = 0 + 3x
-2w = 0 + 3x
Remove the zero:
-2w = 3x

Divide each side by '-2'.
w = -1.5x

Simplifying
w = -1.5x

Subproblem 2
Set the factor '(3w + -8x)' equal to zero and attempt to solve:

Simplifying
3w + -8x = 0

Solving
3w + -8x = 0

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

Add '8x' to each side of the equation.
3w + -8x + 8x = 0 + 8x

Combine like terms: -8x + 8x = 0
3w + 0 = 0 + 8x
3w = 0 + 8x
Remove the zero:
3w = 8x

Divide each side by '3'.
w = 2.666666667x

Simplifying
w = 2.666666667x
Solution
w = {-1.5x, 2.666666667x}

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