2x(x+18)-x(4x-2)=0

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Solution for 2x(x+18)-x(4x-2)=0 equation: 


Simplifying
2x(x + 18) + -1x(4x + -2) = 0

Reorder the terms:
2x(18 + x) + -1x(4x + -2) = 0
(18 * 2x + x * 2x) + -1x(4x + -2) = 0
(36x + 2x2) + -1x(4x + -2) = 0

Reorder the terms:
36x + 2x2 + -1x(-2 + 4x) = 0
36x + 2x2 + (-2 * -1x + 4x * -1x) = 0
36x + 2x2 + (2x + -4x2) = 0

Reorder the terms:
36x + 2x + 2x2 + -4x2 = 0

Combine like terms: 36x + 2x = 38x
38x + 2x2 + -4x2 = 0

Combine like terms: 2x2 + -4x2 = -2x2
38x + -2x2 = 0

Solving
38x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(19 + -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 '(19 + -1x)' equal to zero and attempt to solve:

Simplifying
19 + -1x = 0

Solving
19 + -1x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1x = 0 + -19
-1x = 0 + -19

Combine like terms: 0 + -19 = -19
-1x = -19

Divide each side by '-1'.
x = 19

Simplifying
x = 19
Solution
x = {0, 19}

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