4x(2x+5y)-2x(5x-8y)=

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Solution for 4x(2x+5y)-2x(5x-8y)= equation: 


Simplifying
4x(2x + 5y) + -2x(5x + -8y) = 0
(2x * 4x + 5y * 4x) + -2x(5x + -8y) = 0

Reorder the terms:
(20xy + 8x2) + -2x(5x + -8y) = 0
(20xy + 8x2) + -2x(5x + -8y) = 0
20xy + 8x2 + (5x * -2x + -8y * -2x) = 0

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

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

Combine like terms: 20xy + 16xy = 36xy
36xy + 8x2 + -10x2 = 0

Combine like terms: 8x2 + -10x2 = -2x2
36xy + -2x2 = 0

Solving
36xy + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(18y + -1x) = 0

Ignore the factor 2.

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 '(18y + -1x)' equal to zero and attempt to solve:

Simplifying
18y + -1x = 0

Reorder the terms:
-1x + 18y = 0

Solving
-1x + 18y = 0

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

Add '-18y' to each side of the equation.
-1x + 18y + -18y = 0 + -18y

Combine like terms: 18y + -18y = 0
-1x + 0 = 0 + -18y
-1x = 0 + -18y
Remove the zero:
-1x = -18y

Divide each side by '-1'.
x = 18y

Simplifying
x = 18y
Solution
x = {0, 18y}

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