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

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


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

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

Reorder the terms:
((12xy + 28x2) + 5y * (7x + 3y)) = 0
((12xy + 28x2) + 5y * (7x + 3y)) = 0
(12xy + 28x2 + (7x * 5y + 3y * 5y)) = 0
(12xy + 28x2 + (35xy + 15y2)) = 0

Reorder the terms:
(12xy + 35xy + 28x2 + 15y2) = 0

Combine like terms: 12xy + 35xy = 47xy
(47xy + 28x2 + 15y2) = 0

Solving
47xy + 28x2 + 15y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(7x + 3y)' equal to zero and attempt to solve:

Simplifying
7x + 3y = 0

Solving
7x + 3y = 0

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

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

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

Divide each side by '7'.
x = -0.4285714286y

Simplifying
x = -0.4285714286y

Subproblem 2
Set the factor '(4x + 5y)' equal to zero and attempt to solve:

Simplifying
4x + 5y = 0

Solving
4x + 5y = 0

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

Add '-5y' to each side of the equation.
4x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
4x + 0 = 0 + -5y
4x = 0 + -5y
Remove the zero:
4x = -5y

Divide each side by '4'.
x = -1.25y

Simplifying
x = -1.25y
Solution
x = {-0.4285714286y, -1.25y}

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