(X-2)x(5-X)=0

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Solution for (X-2)x(5-X)=0 equation: 


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

Reorder the terms:
(-2 + X) * x(5 + -1X) = 0

Reorder the terms for easier multiplication:
x(-2 + X)(5 + -1X) = 0

Multiply (-2 + X) * (5 + -1X)
x(-2(5 + -1X) + X(5 + -1X)) = 0
x((5 * -2 + -1X * -2) + X(5 + -1X)) = 0
x((-10 + 2X) + X(5 + -1X)) = 0
x(-10 + 2X + (5 * X + -1X * X)) = 0
x(-10 + 2X + (5X + -1X2)) = 0

Combine like terms: 2X + 5X = 7X
x(-10 + 7X + -1X2) = 0
(-10 * x + 7X * x + -1X2 * x) = 0
(-10x + 7xX + -1xX2) = 0

Solving
-10x + 7xX + -1xX2 = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-10 + 7X + -1X2) = 0

Factor a trinomial.
x((-5 + X)(2 + -1X)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-5 + X)' equal to zero and attempt to solve:

Simplifying
-5 + X = 0

Solving
-5 + X = 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 + X = 0 + 5

Combine like terms: -5 + 5 = 0
0 + X = 0 + 5
X = 0 + 5

Combine like terms: 0 + 5 = 5
X = 5

Add '-1X' to each side of the equation.
X + -1X = 5 + -1X

Combine like terms: X + -1X = 0
0 = 5 + -1X

Simplifying
0 = 5 + -1X

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
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

Add 'X' to each side of the equation.
-1X + X = -2 + X

Combine like terms: -1X + X = 0
0 = -2 + X

Simplifying
0 = -2 + X

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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