(2x-3)(5-x)-x(5-x)=0

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Solution for (2x-3)(5-x)-x(5-x)=0 equation: 


Simplifying
(2x + -3)(5 + -1x) + -1x(5 + -1x) = 0

Reorder the terms:
(-3 + 2x)(5 + -1x) + -1x(5 + -1x) = 0

Multiply (-3 + 2x) * (5 + -1x)
(-3(5 + -1x) + 2x * (5 + -1x)) + -1x(5 + -1x) = 0
((5 * -3 + -1x * -3) + 2x * (5 + -1x)) + -1x(5 + -1x) = 0
((-15 + 3x) + 2x * (5 + -1x)) + -1x(5 + -1x) = 0
(-15 + 3x + (5 * 2x + -1x * 2x)) + -1x(5 + -1x) = 0
(-15 + 3x + (10x + -2x2)) + -1x(5 + -1x) = 0

Combine like terms: 3x + 10x = 13x
(-15 + 13x + -2x2) + -1x(5 + -1x) = 0
-15 + 13x + -2x2 + (5 * -1x + -1x * -1x) = 0
-15 + 13x + -2x2 + (-5x + 1x2) = 0

Reorder the terms:
-15 + 13x + -5x + -2x2 + 1x2 = 0

Combine like terms: 13x + -5x = 8x
-15 + 8x + -2x2 + 1x2 = 0

Combine like terms: -2x2 + 1x2 = -1x2
-15 + 8x + -1x2 = 0

Solving
-15 + 8x + -1x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

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

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

Combine like terms: 0 + 5 = 5
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}

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