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

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


Simplifying
(3 + -1x)(5 + -1x) = 3 + -2x + x2

Multiply (3 + -1x) * (5 + -1x)
(3(5 + -1x) + -1x * (5 + -1x)) = 3 + -2x + x2
((5 * 3 + -1x * 3) + -1x * (5 + -1x)) = 3 + -2x + x2
((15 + -3x) + -1x * (5 + -1x)) = 3 + -2x + x2
(15 + -3x + (5 * -1x + -1x * -1x)) = 3 + -2x + x2
(15 + -3x + (-5x + 1x2)) = 3 + -2x + x2

Combine like terms: -3x + -5x = -8x
(15 + -8x + 1x2) = 3 + -2x + x2

Solving
15 + -8x + 1x2 = 3 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
15 + -3 + -8x + 2x + 1x2 + -1x2 = 3 + -2x + x2 + -3 + 2x + -1x2

Combine like terms: 15 + -3 = 12
12 + -8x + 2x + 1x2 + -1x2 = 3 + -2x + x2 + -3 + 2x + -1x2

Combine like terms: -8x + 2x = -6x
12 + -6x + 1x2 + -1x2 = 3 + -2x + x2 + -3 + 2x + -1x2

Combine like terms: 1x2 + -1x2 = 0
12 + -6x + 0 = 3 + -2x + x2 + -3 + 2x + -1x2
12 + -6x = 3 + -2x + x2 + -3 + 2x + -1x2

Reorder the terms:
12 + -6x = 3 + -3 + -2x + 2x + x2 + -1x2

Combine like terms: 3 + -3 = 0
12 + -6x = 0 + -2x + 2x + x2 + -1x2
12 + -6x = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
12 + -6x = 0 + x2 + -1x2
12 + -6x = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -6x = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(2 + -1x) = 0

Ignore the factor 6.

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
Solution
x = {2}

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