2(X-1)(X-3)=-X

Solution for 2(X-1)(X-3)=-X equation:

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

Reorder the terms:
2(-1 + X)(X + -3) = -1X

Reorder the terms:
2(-1 + X)(-3 + X) = -1X

Multiply (-1 + X) * (-3 + X)
2(-1(-3 + X) + X(-3 + X)) = -1X
2((-3 * -1 + X * -1) + X(-3 + X)) = -1X
2((3 + -1X) + X(-3 + X)) = -1X
2(3 + -1X + (-3 * X + X * X)) = -1X
2(3 + -1X + (-3X + X2)) = -1X

Combine like terms: -1X + -3X = -4X
2(3 + -4X + X2) = -1X
(3 * 2 + -4X * 2 + X2 * 2) = -1X
(6 + -8X + 2X2) = -1X

Solving
6 + -8X + 2X2 = -1X

Solving for variable 'X'.

Reorder the terms:
6 + -8X + X + 2X2 = -1X + X

Combine like terms: -8X + X = -7X
6 + -7X + 2X2 = -1X + X

Combine like terms: -1X + X = 0
6 + -7X + 2X2 = 0

Factor a trinomial.
(3 + -2X)(2 + -1X) = 0

Subproblem 1
Set the factor '(3 + -2X)' equal to zero and attempt to solve:

Simplifying
3 + -2X = 0

Solving
3 + -2X = 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 + -2X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2X = 0 + -3
-2X = 0 + -3

Combine like terms: 0 + -3 = -3
-2X = -3

Divide each side by '-2'.
X = 1.5

Simplifying
X = 1.5
Subproblem 2
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 = {1.5, 2}