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

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


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

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

Remove parenthesis around (2x)
(-5 + x) * 2x = (x + -5)(4)

Reorder the terms for easier multiplication:
2x(-5 + x) = (x + -5)(4)
(-5 * 2x + x * 2x) = (x + -5)(4)
(-10x + 2x2) = (x + -5)(4)

Reorder the terms:
-10x + 2x2 = (-5 + x)(4)

Reorder the terms for easier multiplication:
-10x + 2x2 = 4(-5 + x)
-10x + 2x2 = (-5 * 4 + x * 4)
-10x + 2x2 = (-20 + 4x)

Solving
-10x + 2x2 = -20 + 4x

Solving for variable 'x'.

Reorder the terms:
20 + -10x + -4x + 2x2 = -20 + 4x + 20 + -4x

Combine like terms: -10x + -4x = -14x
20 + -14x + 2x2 = -20 + 4x + 20 + -4x

Reorder the terms:
20 + -14x + 2x2 = -20 + 20 + 4x + -4x

Combine like terms: -20 + 20 = 0
20 + -14x + 2x2 = 0 + 4x + -4x
20 + -14x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
20 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -7x + x2) = 0

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

Ignore the factor 2.

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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