X^2-5=(X-5)(2X-1)

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Solution for X^2-5=(X-5)(2X-1) equation: 


Simplifying
X2 + -5 = (X + -5)(2X + -1)

Reorder the terms:
-5 + X2 = (X + -5)(2X + -1)

Reorder the terms:
-5 + X2 = (-5 + X)(2X + -1)

Reorder the terms:
-5 + X2 = (-5 + X)(-1 + 2X)

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

Combine like terms: -10X + -1X = -11X
-5 + X2 = (5 + -11X + 2X2)

Solving
-5 + X2 = 5 + -11X + 2X2

Solving for variable 'X'.

Reorder the terms:
-5 + -5 + 11X + X2 + -2X2 = 5 + -11X + 2X2 + -5 + 11X + -2X2

Combine like terms: -5 + -5 = -10
-10 + 11X + X2 + -2X2 = 5 + -11X + 2X2 + -5 + 11X + -2X2

Combine like terms: X2 + -2X2 = -1X2
-10 + 11X + -1X2 = 5 + -11X + 2X2 + -5 + 11X + -2X2

Reorder the terms:
-10 + 11X + -1X2 = 5 + -5 + -11X + 11X + 2X2 + -2X2

Combine like terms: 5 + -5 = 0
-10 + 11X + -1X2 = 0 + -11X + 11X + 2X2 + -2X2
-10 + 11X + -1X2 = -11X + 11X + 2X2 + -2X2

Combine like terms: -11X + 11X = 0
-10 + 11X + -1X2 = 0 + 2X2 + -2X2
-10 + 11X + -1X2 = 2X2 + -2X2

Combine like terms: 2X2 + -2X2 = 0
-10 + 11X + -1X2 = 0

Factor a trinomial.
(-10 + X)(1 + -1X) = 0


Subproblem 1
Set the factor '(-10 + X)' equal to zero and attempt to solve:

Simplifying
-10 + X = 0

Solving
-10 + X = 0

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

Add '10' to each side of the equation.
-10 + 10 + X = 0 + 10

Combine like terms: -10 + 10 = 0
0 + X = 0 + 10
X = 0 + 10

Combine like terms: 0 + 10 = 10
X = 10

Simplifying
X = 10

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 = {10, 1}

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