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

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


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

Reorder the terms:
2(-2 + x) = (2x + -1)(x + -3)
(-2 * 2 + x * 2) = (2x + -1)(x + -3)
(-4 + 2x) = (2x + -1)(x + -3)

Reorder the terms:
-4 + 2x = (-1 + 2x)(x + -3)

Reorder the terms:
-4 + 2x = (-1 + 2x)(-3 + x)

Multiply (-1 + 2x) * (-3 + x)
-4 + 2x = (-1(-3 + x) + 2x * (-3 + x))
-4 + 2x = ((-3 * -1 + x * -1) + 2x * (-3 + x))
-4 + 2x = ((3 + -1x) + 2x * (-3 + x))
-4 + 2x = (3 + -1x + (-3 * 2x + x * 2x))
-4 + 2x = (3 + -1x + (-6x + 2x2))

Combine like terms: -1x + -6x = -7x
-4 + 2x = (3 + -7x + 2x2)

Solving
-4 + 2x = 3 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-4 + -3 + 2x + 7x + -2x2 = 3 + -7x + 2x2 + -3 + 7x + -2x2

Combine like terms: -4 + -3 = -7
-7 + 2x + 7x + -2x2 = 3 + -7x + 2x2 + -3 + 7x + -2x2

Combine like terms: 2x + 7x = 9x
-7 + 9x + -2x2 = 3 + -7x + 2x2 + -3 + 7x + -2x2

Reorder the terms:
-7 + 9x + -2x2 = 3 + -3 + -7x + 7x + 2x2 + -2x2

Combine like terms: 3 + -3 = 0
-7 + 9x + -2x2 = 0 + -7x + 7x + 2x2 + -2x2
-7 + 9x + -2x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
-7 + 9x + -2x2 = 0 + 2x2 + -2x2
-7 + 9x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-7 + 9x + -2x2 = 0

Factor a trinomial.
(-7 + 2x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-7 + 2x)' equal to zero and attempt to solve:

Simplifying
-7 + 2x = 0

Solving
-7 + 2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2x = 0 + 7
2x = 0 + 7

Combine like terms: 0 + 7 = 7
2x = 7

Divide each side by '2'.
x = 3.5

Simplifying
x = 3.5

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 = {3.5, 1}

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