0=(4x-1)(x-1)

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Solution for 0=(4x-1)(x-1) equation: 


Simplifying
0 = (4x + -1)(x + -1)

Reorder the terms:
0 = (-1 + 4x)(x + -1)

Reorder the terms:
0 = (-1 + 4x)(-1 + x)

Multiply (-1 + 4x) * (-1 + x)
0 = (-1(-1 + x) + 4x * (-1 + x))
0 = ((-1 * -1 + x * -1) + 4x * (-1 + x))
0 = ((1 + -1x) + 4x * (-1 + x))
0 = (1 + -1x + (-1 * 4x + x * 4x))
0 = (1 + -1x + (-4x + 4x2))

Combine like terms: -1x + -4x = -5x
0 = (1 + -5x + 4x2)

Solving
0 = 1 + -5x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + 5x + -4x2 = 1 + -5x + 4x2 + -1 + 5x + -4x2

Reorder the terms:
-1 + 5x + -4x2 = 1 + -1 + -5x + 5x + 4x2 + -4x2

Combine like terms: 1 + -1 = 0
-1 + 5x + -4x2 = 0 + -5x + 5x + 4x2 + -4x2
-1 + 5x + -4x2 = -5x + 5x + 4x2 + -4x2

Combine like terms: -5x + 5x = 0
-1 + 5x + -4x2 = 0 + 4x2 + -4x2
-1 + 5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-1 + 5x + -4x2 = 0

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


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

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1

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

Simplifying
1 + -4x = 0

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

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

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

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {1, 0.25}

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