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

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

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

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

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

Solving
-6 + 2x = -3x + -1x2

Solving for variable 'x'.

Combine like terms: 2x + 3x = 5x
-6 + 5x + x2 = -3x + -1x2 + 3x + x2

Reorder the terms:
-6 + 5x + x2 = -3x + 3x + -1x2 + x2

Combine like terms: -3x + 3x = 0
-6 + 5x + x2 = 0 + -1x2 + x2
-6 + 5x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-6 + 5x + x2 = 0

Factor a trinomial.
(-6 + -1x)(1 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-6, 1}