2x(x-3)=x-5

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Solution for 2x(x-3)=x-5 equation: 


Simplifying
2x(x + -3) = x + -5

Reorder the terms:
2x(-3 + x) = x + -5
(-3 * 2x + x * 2x) = x + -5
(-6x + 2x2) = x + -5

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

Solving
-6x + 2x2 = -5 + x

Solving for variable 'x'.

Reorder the terms:
5 + -6x + -1x + 2x2 = -5 + x + 5 + -1x

Combine like terms: -6x + -1x = -7x
5 + -7x + 2x2 = -5 + x + 5 + -1x

Reorder the terms:
5 + -7x + 2x2 = -5 + 5 + x + -1x

Combine like terms: -5 + 5 = 0
5 + -7x + 2x2 = 0 + x + -1x
5 + -7x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
5 + -7x + 2x2 = 0

Factor a trinomial.
(1 + -1x)(5 + -2x) = 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 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

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

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

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {1, 2.5}

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