2(10-x)=(x-3)(x)

Solution for 2(10-x)=(x-3)(x) equation:

Simplifying
2(10 + -1x) = (x + -3)(x)
(10 * 2 + -1x * 2) = (x + -3)(x)
(20 + -2x) = (x + -3)(x)

Reorder the terms:
20 + -2x = (-3 + x)(x)

Reorder the terms for easier multiplication:
20 + -2x = x(-3 + x)
20 + -2x = (-3 * x + x * x)
20 + -2x = (-3x + x2)

Solving
20 + -2x = -3x + x2

Solving for variable 'x'.

Combine like terms: -2x + 3x = 1x
20 + 1x + -1x2 = -3x + x2 + 3x + -1x2

Reorder the terms:
20 + 1x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
20 + 1x + -1x2 = 0 + x2 + -1x2
20 + 1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
20 + 1x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(4 + x) = 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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {5, -4}