X(X-2)-3(X-2)=0

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Solution for X(X-2)-3(X-2)=0 equation:


Simplifying
X(X + -2) + -3(X + -2) = 0

Reorder the terms:
X(-2 + X) + -3(X + -2) = 0
(-2 * X + X * X) + -3(X + -2) = 0
(-2X + X2) + -3(X + -2) = 0

Reorder the terms:
-2X + X2 + -3(-2 + X) = 0
-2X + X2 + (-2 * -3 + X * -3) = 0
-2X + X2 + (6 + -3X) = 0

Reorder the terms:
6 + -2X + -3X + X2 = 0

Combine like terms: -2X + -3X = -5X
6 + -5X + X2 = 0

Solving
6 + -5X + X2 = 0

Solving for variable 'X'.

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

Subproblem 1

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

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 = {2, 3}

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