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

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


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

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

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

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

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

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

Remove parenthesis around (-4 + x)
4 + -9x + 2x2 = -4 + x

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

Solving for variable 'x'.

Reorder the terms:
4 + 4 + -9x + -1x + 2x2 = -4 + x + 4 + -1x

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

Combine like terms: -9x + -1x = -10x
8 + -10x + 2x2 = -4 + x + 4 + -1x

Reorder the terms:
8 + -10x + 2x2 = -4 + 4 + x + -1x

Combine like terms: -4 + 4 = 0
8 + -10x + 2x2 = 0 + x + -1x
8 + -10x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
8 + -10x + 2x2 = 0

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

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {1, 4}

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