(x-3)2-(x-1)(3-x)=2(3-x)2

Solution for (x-3)2-(x-1)(3-x)=2(3-x)2 equation:

Simplifying
(x + -3) * 2 + -1(x + -1)(3 + -1x) = 2(3 + -1x) * 2

Reorder the terms:
(-3 + x) * 2 + -1(x + -1)(3 + -1x) = 2(3 + -1x) * 2

Reorder the terms for easier multiplication:
2(-3 + x) + -1(x + -1)(3 + -1x) = 2(3 + -1x) * 2
(-3 * 2 + x * 2) + -1(x + -1)(3 + -1x) = 2(3 + -1x) * 2
(-6 + 2x) + -1(x + -1)(3 + -1x) = 2(3 + -1x) * 2

Reorder the terms:
-6 + 2x + -1(-1 + x)(3 + -1x) = 2(3 + -1x) * 2

Multiply (-1 + x) * (3 + -1x)
-6 + 2x + -1(-1(3 + -1x) + x(3 + -1x)) = 2(3 + -1x) * 2
-6 + 2x + -1((3 * -1 + -1x * -1) + x(3 + -1x)) = 2(3 + -1x) * 2
-6 + 2x + -1((-3 + 1x) + x(3 + -1x)) = 2(3 + -1x) * 2
-6 + 2x + -1(-3 + 1x + (3 * x + -1x * x)) = 2(3 + -1x) * 2
-6 + 2x + -1(-3 + 1x + (3x + -1x2)) = 2(3 + -1x) * 2

Combine like terms: 1x + 3x = 4x
-6 + 2x + -1(-3 + 4x + -1x2) = 2(3 + -1x) * 2
-6 + 2x + (-3 * -1 + 4x * -1 + -1x2 * -1) = 2(3 + -1x) * 2
-6 + 2x + (3 + -4x + 1x2) = 2(3 + -1x) * 2

Reorder the terms:
-6 + 3 + 2x + -4x + 1x2 = 2(3 + -1x) * 2

Combine like terms: -6 + 3 = -3
-3 + 2x + -4x + 1x2 = 2(3 + -1x) * 2

Combine like terms: 2x + -4x = -2x
-3 + -2x + 1x2 = 2(3 + -1x) * 2

Reorder the terms for easier multiplication:
-3 + -2x + 1x2 = 2 * 2(3 + -1x)

Multiply 2 * 2
-3 + -2x + 1x2 = 4(3 + -1x)
-3 + -2x + 1x2 = (3 * 4 + -1x * 4)
-3 + -2x + 1x2 = (12 + -4x)

Solving
-3 + -2x + 1x2 = 12 + -4x

Solving for variable 'x'.

Reorder the terms:
-3 + -12 + -2x + 4x + 1x2 = 12 + -4x + -12 + 4x

Combine like terms: -3 + -12 = -15
-15 + -2x + 4x + 1x2 = 12 + -4x + -12 + 4x

Combine like terms: -2x + 4x = 2x
-15 + 2x + 1x2 = 12 + -4x + -12 + 4x

Reorder the terms:
-15 + 2x + 1x2 = 12 + -12 + -4x + 4x

Combine like terms: 12 + -12 = 0
-15 + 2x + 1x2 = 0 + -4x + 4x
-15 + 2x + 1x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-15 + 2x + 1x2 = 0

Factor a trinomial.
(-5 + -1x)(3 + -1x) = 0

Subproblem 1
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
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 = {-5, 3}