(x+4y)(x-10y)=

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


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

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

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

Reorder the terms:
(-10xy + 4xy + x2 + -40y2) = 0

Combine like terms: -10xy + 4xy = -6xy
(-6xy + x2 + -40y2) = 0

Solving
-6xy + x2 + -40y2 = 0

Solving for variable 'x'.

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


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

Simplifying
x + -10y = 0

Solving
x + -10y = 0

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

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

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

Simplifying
x = 10y

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

Simplifying
x + 4y = 0

Solving
x + 4y = 0

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

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

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

Simplifying
x = -4y
Solution
x = {10y, -4y}

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