(2x-3w)(6x+w)=0

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Solution for (2x-3w)(6x+w)=0 equation: 


Simplifying
(2x + -3w)(6x + w) = 0

Reorder the terms:
(-3w + 2x)(6x + w) = 0

Reorder the terms:
(-3w + 2x)(w + 6x) = 0

Multiply (-3w + 2x) * (w + 6x)
(-3w * (w + 6x) + 2x * (w + 6x)) = 0
((w * -3w + 6x * -3w) + 2x * (w + 6x)) = 0

Reorder the terms:
((-18wx + -3w2) + 2x * (w + 6x)) = 0
((-18wx + -3w2) + 2x * (w + 6x)) = 0
(-18wx + -3w2 + (w * 2x + 6x * 2x)) = 0
(-18wx + -3w2 + (2wx + 12x2)) = 0

Reorder the terms:
(-18wx + 2wx + -3w2 + 12x2) = 0

Combine like terms: -18wx + 2wx = -16wx
(-16wx + -3w2 + 12x2) = 0

Solving
-16wx + -3w2 + 12x2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1w + -6x)(3w + -2x) = 0


Subproblem 1
Set the factor '(-1w + -6x)' equal to zero and attempt to solve:

Simplifying
-1w + -6x = 0

Solving
-1w + -6x = 0

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

Add '6x' to each side of the equation.
-1w + -6x + 6x = 0 + 6x

Combine like terms: -6x + 6x = 0
-1w + 0 = 0 + 6x
-1w = 0 + 6x
Remove the zero:
-1w = 6x

Divide each side by '-1'.
w = -6x

Simplifying
w = -6x

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

Simplifying
3w + -2x = 0

Solving
3w + -2x = 0

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

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

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

Divide each side by '3'.
w = 0.6666666667x

Simplifying
w = 0.6666666667x
Solution
w = {-6x, 0.6666666667x}

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