(x-2)x-(x-2)5=0

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Solution for (x-2)x-(x-2)5=0 equation: 


Simplifying
(x + -2) * x + -1(x + -2) * 5 = 0

Reorder the terms:
(-2 + x) * x + -1(x + -2) * 5 = 0

Reorder the terms for easier multiplication:
x(-2 + x) + -1(x + -2) * 5 = 0
(-2 * x + x * x) + -1(x + -2) * 5 = 0
(-2x + x2) + -1(x + -2) * 5 = 0

Reorder the terms:
-2x + x2 + -1(-2 + x) * 5 = 0

Reorder the terms for easier multiplication:
-2x + x2 + -1 * 5(-2 + x) = 0

Multiply -1 * 5
-2x + x2 + -5(-2 + x) = 0
-2x + x2 + (-2 * -5 + x * -5) = 0
-2x + x2 + (10 + -5x) = 0

Reorder the terms:
10 + -2x + -5x + x2 = 0

Combine like terms: -2x + -5x = -7x
10 + -7x + x2 = 0

Solving
10 + -7x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(5 + -1x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, 5}

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