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

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


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

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

Reorder the terms:
((-8xy + 28x2) + 5y * (7x + -2y)) = 0
((-8xy + 28x2) + 5y * (7x + -2y)) = 0
(-8xy + 28x2 + (7x * 5y + -2y * 5y)) = 0
(-8xy + 28x2 + (35xy + -10y2)) = 0

Reorder the terms:
(-8xy + 35xy + 28x2 + -10y2) = 0

Combine like terms: -8xy + 35xy = 27xy
(27xy + 28x2 + -10y2) = 0

Solving
27xy + 28x2 + -10y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7x + -2y)(4x + 5y) = 0


Subproblem 1
Set the factor '(7x + -2y)' equal to zero and attempt to solve:

Simplifying
7x + -2y = 0

Solving
7x + -2y = 0

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

Add '2y' to each side of the equation.
7x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
7x + 0 = 0 + 2y
7x = 0 + 2y
Remove the zero:
7x = 2y

Divide each side by '7'.
x = 0.2857142857y

Simplifying
x = 0.2857142857y

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 = {0.2857142857y, -1.25y}

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