(x-1)2-(5-x)(x-1)=0

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Solution for (x-1)2-(5-x)(x-1)=0 equation:


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

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

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

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

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

Combine like terms: 5x + 1x = 6x
-2 + 2x + -1(-5 + 6x + -1x2) = 0
-2 + 2x + (-5 * -1 + 6x * -1 + -1x2 * -1) = 0
-2 + 2x + (5 + -6x + 1x2) = 0

Reorder the terms:
-2 + 5 + 2x + -6x + 1x2 = 0

Combine like terms: -2 + 5 = 3
3 + 2x + -6x + 1x2 = 0

Combine like terms: 2x + -6x = -4x
3 + -4x + 1x2 = 0

Solving
3 + -4x + 1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(3 + -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 '(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 = {1, 3}

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