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

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

Simplifying
x(3 + -1x) + 2(x2 + -5x + 3) = 0
(3 * x + -1x * x) + 2(x2 + -5x + 3) = 0
(3x + -1x2) + 2(x2 + -5x + 3) = 0

Reorder the terms:
3x + -1x2 + 2(3 + -5x + x2) = 0
3x + -1x2 + (3 * 2 + -5x * 2 + x2 * 2) = 0
3x + -1x2 + (6 + -10x + 2x2) = 0

Reorder the terms:
6 + 3x + -10x + -1x2 + 2x2 = 0

Combine like terms: 3x + -10x = -7x
6 + -7x + -1x2 + 2x2 = 0

Combine like terms: -1x2 + 2x2 = 1x2
6 + -7x + 1x2 = 0

Solving
6 + -7x + 1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {1, 6}