x(x-4)=2x-5

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


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

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

Reorder the terms:
-4x + x2 = -5 + 2x

Solving
-4x + x2 = -5 + 2x

Solving for variable 'x'.

Reorder the terms:
5 + -4x + -2x + x2 = -5 + 2x + 5 + -2x

Combine like terms: -4x + -2x = -6x
5 + -6x + x2 = -5 + 2x + 5 + -2x

Reorder the terms:
5 + -6x + x2 = -5 + 5 + 2x + -2x

Combine like terms: -5 + 5 = 0
5 + -6x + x2 = 0 + 2x + -2x
5 + -6x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
5 + -6x + x2 = 0

Factor a trinomial.
(1 + -1x)(5 + -1x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1, 5}

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