(3x-4w)(5x+7w)=0

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Solution for (3x-4w)(5x+7w)=0 equation: 


Simplifying
(3x + -4w)(5x + 7w) = 0

Reorder the terms:
(-4w + 3x)(5x + 7w) = 0

Reorder the terms:
(-4w + 3x)(7w + 5x) = 0

Multiply (-4w + 3x) * (7w + 5x)
(-4w * (7w + 5x) + 3x * (7w + 5x)) = 0
((7w * -4w + 5x * -4w) + 3x * (7w + 5x)) = 0

Reorder the terms:
((-20wx + -28w2) + 3x * (7w + 5x)) = 0
((-20wx + -28w2) + 3x * (7w + 5x)) = 0
(-20wx + -28w2 + (7w * 3x + 5x * 3x)) = 0
(-20wx + -28w2 + (21wx + 15x2)) = 0

Reorder the terms:
(-20wx + 21wx + -28w2 + 15x2) = 0

Combine like terms: -20wx + 21wx = 1wx
(1wx + -28w2 + 15x2) = 0

Solving
1wx + -28w2 + 15x2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7w + -5x)(4w + -3x) = 0


Subproblem 1
Set the factor '(-7w + -5x)' equal to zero and attempt to solve:

Simplifying
-7w + -5x = 0

Solving
-7w + -5x = 0

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

Add '5x' to each side of the equation.
-7w + -5x + 5x = 0 + 5x

Combine like terms: -5x + 5x = 0
-7w + 0 = 0 + 5x
-7w = 0 + 5x
Remove the zero:
-7w = 5x

Divide each side by '-7'.
w = -0.7142857143x

Simplifying
w = -0.7142857143x

Subproblem 2
Set the factor '(4w + -3x)' equal to zero and attempt to solve:

Simplifying
4w + -3x = 0

Solving
4w + -3x = 0

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

Add '3x' to each side of the equation.
4w + -3x + 3x = 0 + 3x

Combine like terms: -3x + 3x = 0
4w + 0 = 0 + 3x
4w = 0 + 3x
Remove the zero:
4w = 3x

Divide each side by '4'.
w = 0.75x

Simplifying
w = 0.75x
Solution
w = {-0.7142857143x, 0.75x}

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