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

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


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

Reorder the terms:
-4x(-2 + x) + 5x = x
(-2 * -4x + x * -4x) + 5x = x
(8x + -4x2) + 5x = x

Reorder the terms:
8x + 5x + -4x2 = x

Combine like terms: 8x + 5x = 13x
13x + -4x2 = x

Solving
13x + -4x2 = x

Solving for variable 'x'.

Reorder the terms:
13x + -1x + -4x2 = x + -1x

Combine like terms: 13x + -1x = 12x
12x + -4x2 = x + -1x

Combine like terms: x + -1x = 0
12x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(3 + -1x) = 0

Ignore the factor 4.

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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, 3}

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