(3x+4y)(7x-5y)=

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


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

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

Reorder the terms:
((-15xy + 21x2) + 4y * (7x + -5y)) = 0
((-15xy + 21x2) + 4y * (7x + -5y)) = 0
(-15xy + 21x2 + (7x * 4y + -5y * 4y)) = 0
(-15xy + 21x2 + (28xy + -20y2)) = 0

Reorder the terms:
(-15xy + 28xy + 21x2 + -20y2) = 0

Combine like terms: -15xy + 28xy = 13xy
(13xy + 21x2 + -20y2) = 0

Solving
13xy + 21x2 + -20y2 = 0

Solving for variable 'x'.

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


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

Simplifying
7x + -5y = 0

Solving
7x + -5y = 0

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

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

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

Divide each side by '7'.
x = 0.7142857143y

Simplifying
x = 0.7142857143y

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

Simplifying
3x + 4y = 0

Solving
3x + 4y = 0

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

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

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

Divide each side by '3'.
x = -1.333333333y

Simplifying
x = -1.333333333y
Solution
x = {0.7142857143y, -1.333333333y}

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