=(3x-5w)(7x-w)

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Solution for =(3x-5w)(7x-w) equation: 


Simplifying
0 = (3x + -5w)(7x + -1w)

Reorder the terms:
0 = (-5w + 3x)(7x + -1w)

Reorder the terms:
0 = (-5w + 3x)(-1w + 7x)

Multiply (-5w + 3x) * (-1w + 7x)
0 = (-5w * (-1w + 7x) + 3x * (-1w + 7x))
0 = ((-1w * -5w + 7x * -5w) + 3x * (-1w + 7x))

Reorder the terms:
0 = ((-35wx + 5w2) + 3x * (-1w + 7x))
0 = ((-35wx + 5w2) + 3x * (-1w + 7x))
0 = (-35wx + 5w2 + (-1w * 3x + 7x * 3x))
0 = (-35wx + 5w2 + (-3wx + 21x2))

Reorder the terms:
0 = (-35wx + -3wx + 5w2 + 21x2)

Combine like terms: -35wx + -3wx = -38wx
0 = (-38wx + 5w2 + 21x2)

Solving
0 = -38wx + 5w2 + 21x2

Solving for variable 'w'.
Remove the zero:
38wx + -5w2 + -21x2 = -38wx + 5w2 + 21x2 + 38wx + -5w2 + -21x2

Reorder the terms:
38wx + -5w2 + -21x2 = -38wx + 38wx + 5w2 + -5w2 + 21x2 + -21x2

Combine like terms: -38wx + 38wx = 0
38wx + -5w2 + -21x2 = 0 + 5w2 + -5w2 + 21x2 + -21x2
38wx + -5w2 + -21x2 = 5w2 + -5w2 + 21x2 + -21x2

Combine like terms: 5w2 + -5w2 = 0
38wx + -5w2 + -21x2 = 0 + 21x2 + -21x2
38wx + -5w2 + -21x2 = 21x2 + -21x2

Combine like terms: 21x2 + -21x2 = 0
38wx + -5w2 + -21x2 = 0

Factor a trinomial.
(-5w + 3x)(w + -7x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(w + -7x)' equal to zero and attempt to solve:

Simplifying
w + -7x = 0

Solving
w + -7x = 0

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

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

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

Simplifying
w = 7x
Solution
w = {0.6x, 7x}

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