x=(x+y+10)(2x)(4y)

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Solution for x=(x+y+10)(2x)(4y) equation: 


Simplifying
x = (x + y + 10)(2x)(4y)

Reorder the terms:
x = (10 + x + y)(2x)(4y)

Remove parenthesis around (2x)
x = (10 + x + y) * 2x(4y)

Remove parenthesis around (4y)
x = (10 + x + y) * 2x * 4y

Reorder the terms for easier multiplication:
x = 2 * 4x * y(10 + x + y)

Multiply 2 * 4
x = 8x * y(10 + x + y)

Multiply x * y
x = 8xy(10 + x + y)
x = (10 * 8xy + x * 8xy + y * 8xy)

Reorder the terms:
x = (80xy + 8xy2 + 8x2y)
x = (80xy + 8xy2 + 8x2y)

Solving
x = 80xy + 8xy2 + 8x2y

Solving for variable 'x'.

Reorder the terms:
x + -80xy + -8xy2 + -8x2y = 80xy + -80xy + 8xy2 + -8xy2 + 8x2y + -8x2y

Combine like terms: 80xy + -80xy = 0
x + -80xy + -8xy2 + -8x2y = 0 + 8xy2 + -8xy2 + 8x2y + -8x2y
x + -80xy + -8xy2 + -8x2y = 8xy2 + -8xy2 + 8x2y + -8x2y

Combine like terms: 8xy2 + -8xy2 = 0
x + -80xy + -8xy2 + -8x2y = 0 + 8x2y + -8x2y
x + -80xy + -8xy2 + -8x2y = 8x2y + -8x2y

Combine like terms: 8x2y + -8x2y = 0
x + -80xy + -8xy2 + -8x2y = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -80y + -8y2 + -8xy) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(1 + -80y + -8y2 + -8xy)' equal to zero and attempt to solve:

Simplifying
1 + -80y + -8y2 + -8xy = 0

Reorder the terms:
1 + -8xy + -80y + -8y2 = 0

Solving
1 + -8xy + -80y + -8y2 = 0

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

Add '-1' to each side of the equation.
1 + -8xy + -80y + -1 + -8y2 = 0 + -1

Reorder the terms:
1 + -1 + -8xy + -80y + -8y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8xy + -80y + -8y2 = 0 + -1
-8xy + -80y + -8y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-8xy + -80y + -8y2 = -1

Add '80y' to each side of the equation.
-8xy + -80y + 80y + -8y2 = -1 + 80y

Combine like terms: -80y + 80y = 0
-8xy + 0 + -8y2 = -1 + 80y
-8xy + -8y2 = -1 + 80y

Add '8y2' to each side of the equation.
-8xy + -8y2 + 8y2 = -1 + 80y + 8y2

Combine like terms: -8y2 + 8y2 = 0
-8xy + 0 = -1 + 80y + 8y2
-8xy = -1 + 80y + 8y2

Divide each side by '-8y'.
x = 0.125y-1 + -10 + -1y

Simplifying
x = 0.125y-1 + -10 + -1y

Reorder the terms:
x = -10 + 0.125y-1 + -1y
Solution
x = {0, -10 + 0.125y-1 + -1y}

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