(3x+7y)*(7x+5y)=

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


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

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

Reorder the terms:
((15xy + 21x2) + 7y * (7x + 5y)) = 0
((15xy + 21x2) + 7y * (7x + 5y)) = 0
(15xy + 21x2 + (7x * 7y + 5y * 7y)) = 0
(15xy + 21x2 + (49xy + 35y2)) = 0

Reorder the terms:
(15xy + 49xy + 21x2 + 35y2) = 0

Combine like terms: 15xy + 49xy = 64xy
(64xy + 21x2 + 35y2) = 0

Solving
64xy + 21x2 + 35y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7x + 5y)(3x + 7y) = 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 + 7y)' equal to zero and attempt to solve:

Simplifying
3x + 7y = 0

Solving
3x + 7y = 0

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

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

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

Divide each side by '3'.
x = -2.333333333y

Simplifying
x = -2.333333333y
Solution
x = {-0.7142857143y, -2.333333333y}

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