(x-4)=(x-4)*(2x-1)

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Solution for (x-4)=(x-4)*(2x-1) equation: 


Simplifying
(x + -4) = (x + -4)(2x + -1)

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

Remove parenthesis around (-4 + x)
-4 + x = (x + -4)(2x + -1)

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

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

Multiply (-4 + x) * (-1 + 2x)
-4 + x = (-4(-1 + 2x) + x(-1 + 2x))
-4 + x = ((-1 * -4 + 2x * -4) + x(-1 + 2x))
-4 + x = ((4 + -8x) + x(-1 + 2x))
-4 + x = (4 + -8x + (-1 * x + 2x * x))
-4 + x = (4 + -8x + (-1x + 2x2))

Combine like terms: -8x + -1x = -9x
-4 + x = (4 + -9x + 2x2)

Solving
-4 + x = 4 + -9x + 2x2

Solving for variable 'x'.

Reorder the terms:
-4 + -4 + x + 9x + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2

Combine like terms: -4 + -4 = -8
-8 + x + 9x + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2

Combine like terms: x + 9x = 10x
-8 + 10x + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2

Reorder the terms:
-8 + 10x + -2x2 = 4 + -4 + -9x + 9x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
-8 + 10x + -2x2 = 0 + -9x + 9x + 2x2 + -2x2
-8 + 10x + -2x2 = -9x + 9x + 2x2 + -2x2

Combine like terms: -9x + 9x = 0
-8 + 10x + -2x2 = 0 + 2x2 + -2x2
-8 + 10x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-8 + 10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 5x + -1x2) = 0

Factor a trinomial.
2((-4 + x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4

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 = {4, 1}

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