(3x-10y)(7x-4y)=

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Solution for (3x-10y)(7x-4y)= equation: 


Simplifying
(3x + -10y)(7x + -4y) = 0

Multiply (3x + -10y) * (7x + -4y)
(3x * (7x + -4y) + -10y * (7x + -4y)) = 0
((7x * 3x + -4y * 3x) + -10y * (7x + -4y)) = 0

Reorder the terms:
((-12xy + 21x2) + -10y * (7x + -4y)) = 0
((-12xy + 21x2) + -10y * (7x + -4y)) = 0
(-12xy + 21x2 + (7x * -10y + -4y * -10y)) = 0
(-12xy + 21x2 + (-70xy + 40y2)) = 0

Reorder the terms:
(-12xy + -70xy + 21x2 + 40y2) = 0

Combine like terms: -12xy + -70xy = -82xy
(-82xy + 21x2 + 40y2) = 0

Solving
-82xy + 21x2 + 40y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -10y)(7x + -4y) = 0


Subproblem 1
Set the factor '(3x + -10y)' equal to zero and attempt to solve:

Simplifying
3x + -10y = 0

Solving
3x + -10y = 0

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

Add '10y' to each side of the equation.
3x + -10y + 10y = 0 + 10y

Combine like terms: -10y + 10y = 0
3x + 0 = 0 + 10y
3x = 0 + 10y
Remove the zero:
3x = 10y

Divide each side by '3'.
x = 3.333333333y

Simplifying
x = 3.333333333y

Subproblem 2
Set the factor '(7x + -4y)' equal to zero and attempt to solve:

Simplifying
7x + -4y = 0

Solving
7x + -4y = 0

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

Add '4y' to each side of the equation.
7x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
7x + 0 = 0 + 4y
7x = 0 + 4y
Remove the zero:
7x = 4y

Divide each side by '7'.
x = 0.5714285714y

Simplifying
x = 0.5714285714y
Solution
x = {3.333333333y, 0.5714285714y}

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