(3x-2w)(7x-3w)=0

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Solution for (3x-2w)(7x-3w)=0 equation: 


Simplifying
(3x + -2w)(7x + -3w) = 0

Reorder the terms:
(-2w + 3x)(7x + -3w) = 0

Reorder the terms:
(-2w + 3x)(-3w + 7x) = 0

Multiply (-2w + 3x) * (-3w + 7x)
(-2w * (-3w + 7x) + 3x * (-3w + 7x)) = 0
((-3w * -2w + 7x * -2w) + 3x * (-3w + 7x)) = 0

Reorder the terms:
((-14wx + 6w2) + 3x * (-3w + 7x)) = 0
((-14wx + 6w2) + 3x * (-3w + 7x)) = 0
(-14wx + 6w2 + (-3w * 3x + 7x * 3x)) = 0
(-14wx + 6w2 + (-9wx + 21x2)) = 0

Reorder the terms:
(-14wx + -9wx + 6w2 + 21x2) = 0

Combine like terms: -14wx + -9wx = -23wx
(-23wx + 6w2 + 21x2) = 0

Solving
-23wx + 6w2 + 21x2 = 0

Solving for variable 'w'.

Factor a trinomial.
(3w + -7x)(2w + -3x) = 0


Subproblem 1
Set the factor '(3w + -7x)' equal to zero and attempt to solve:

Simplifying
3w + -7x = 0

Solving
3w + -7x = 0

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

Add '7x' to each side of the equation.
3w + -7x + 7x = 0 + 7x

Combine like terms: -7x + 7x = 0
3w + 0 = 0 + 7x
3w = 0 + 7x
Remove the zero:
3w = 7x

Divide each side by '3'.
w = 2.333333333x

Simplifying
w = 2.333333333x

Subproblem 2
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
Solution
w = {2.333333333x, 1.5x}

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