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

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


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

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

Reorder the terms:
((-10xy + 8x2) + 4y * (4x + -5y)) = 0
((-10xy + 8x2) + 4y * (4x + -5y)) = 0
(-10xy + 8x2 + (4x * 4y + -5y * 4y)) = 0
(-10xy + 8x2 + (16xy + -20y2)) = 0

Reorder the terms:
(-10xy + 16xy + 8x2 + -20y2) = 0

Combine like terms: -10xy + 16xy = 6xy
(6xy + 8x2 + -20y2) = 0

Solving
6xy + 8x2 + -20y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3xy + 4x2 + -10y2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
x + 2y = 0

Solving
x + 2y = 0

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

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

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

Simplifying
x = -2y
Solution
x = {1.25y, -2y}

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