(4x+2y)(7x-5y)=

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Solution for (4x+2y)(7x-5y)= equation: 


Simplifying
(4x + 2y)(7x + -5y) = 0

Multiply (4x + 2y) * (7x + -5y)
(4x * (7x + -5y) + 2y * (7x + -5y)) = 0
((7x * 4x + -5y * 4x) + 2y * (7x + -5y)) = 0

Reorder the terms:
((-20xy + 28x2) + 2y * (7x + -5y)) = 0
((-20xy + 28x2) + 2y * (7x + -5y)) = 0
(-20xy + 28x2 + (7x * 2y + -5y * 2y)) = 0
(-20xy + 28x2 + (14xy + -10y2)) = 0

Reorder the terms:
(-20xy + 14xy + 28x2 + -10y2) = 0

Combine like terms: -20xy + 14xy = -6xy
(-6xy + 28x2 + -10y2) = 0

Solving
-6xy + 28x2 + -10y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3xy + 14x2 + -5y2) = 0

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

Ignore the factor 2.

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 '(2x + y)' equal to zero and attempt to solve:

Simplifying
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y
Solution
x = {0.7142857143y, -0.5y}

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