x(x-1)=(2x-6)(x-3)

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Solution for x(x-1)=(2x-6)(x-3) equation: 


Simplifying
x(x + -1) = (2x + -6)(x + -3)

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

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

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

Multiply (-6 + 2x) * (-3 + x)
-1x + x2 = (-6(-3 + x) + 2x * (-3 + x))
-1x + x2 = ((-3 * -6 + x * -6) + 2x * (-3 + x))
-1x + x2 = ((18 + -6x) + 2x * (-3 + x))
-1x + x2 = (18 + -6x + (-3 * 2x + x * 2x))
-1x + x2 = (18 + -6x + (-6x + 2x2))

Combine like terms: -6x + -6x = -12x
-1x + x2 = (18 + -12x + 2x2)

Solving
-1x + x2 = 18 + -12x + 2x2

Solving for variable 'x'.

Reorder the terms:
-18 + -1x + 12x + x2 + -2x2 = 18 + -12x + 2x2 + -18 + 12x + -2x2

Combine like terms: -1x + 12x = 11x
-18 + 11x + x2 + -2x2 = 18 + -12x + 2x2 + -18 + 12x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-18 + 11x + -1x2 = 18 + -12x + 2x2 + -18 + 12x + -2x2

Reorder the terms:
-18 + 11x + -1x2 = 18 + -18 + -12x + 12x + 2x2 + -2x2

Combine like terms: 18 + -18 = 0
-18 + 11x + -1x2 = 0 + -12x + 12x + 2x2 + -2x2
-18 + 11x + -1x2 = -12x + 12x + 2x2 + -2x2

Combine like terms: -12x + 12x = 0
-18 + 11x + -1x2 = 0 + 2x2 + -2x2
-18 + 11x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-18 + 11x + -1x2 = 0

Factor a trinomial.
(-9 + x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-9 + x)' equal to zero and attempt to solve:

Simplifying
-9 + x = 0

Solving
-9 + x = 0

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

Add '9' to each side of the equation.
-9 + 9 + x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + x = 0 + 9
x = 0 + 9

Combine like terms: 0 + 9 = 9
x = 9

Simplifying
x = 9

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 = {9, 2}

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