(3x+2y)(5x+7y)=

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Solution for (3x+2y)(5x+7y)= equation: 


Simplifying
(3x + 2y)(5x + 7y) = 0

Multiply (3x + 2y) * (5x + 7y)
(3x * (5x + 7y) + 2y * (5x + 7y)) = 0
((5x * 3x + 7y * 3x) + 2y * (5x + 7y)) = 0

Reorder the terms:
((21xy + 15x2) + 2y * (5x + 7y)) = 0
((21xy + 15x2) + 2y * (5x + 7y)) = 0
(21xy + 15x2 + (5x * 2y + 7y * 2y)) = 0
(21xy + 15x2 + (10xy + 14y2)) = 0

Reorder the terms:
(21xy + 10xy + 15x2 + 14y2) = 0

Combine like terms: 21xy + 10xy = 31xy
(31xy + 15x2 + 14y2) = 0

Solving
31xy + 15x2 + 14y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + 2y)(5x + 7y) = 0


Subproblem 1
Set the factor '(3x + 2y)' equal to zero and attempt to solve:

Simplifying
3x + 2y = 0

Solving
3x + 2y = 0

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

Add '-2y' to each side of the equation.
3x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
3x + 0 = 0 + -2y
3x = 0 + -2y
Remove the zero:
3x = -2y

Divide each side by '3'.
x = -0.6666666667y

Simplifying
x = -0.6666666667y

Subproblem 2
Set the factor '(5x + 7y)' equal to zero and attempt to solve:

Simplifying
5x + 7y = 0

Solving
5x + 7y = 0

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

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

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

Divide each side by '5'.
x = -1.4y

Simplifying
x = -1.4y
Solution
x = {-0.6666666667y, -1.4y}

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