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

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


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

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

Combine like terms: x + 2x = 3x
-1 + 3x = 2x(2x + -1)

Reorder the terms:
-1 + 3x = 2x(-1 + 2x)
-1 + 3x = (-1 * 2x + 2x * 2x)
-1 + 3x = (-2x + 4x2)

Solving
-1 + 3x = -2x + 4x2

Solving for variable 'x'.

Combine like terms: 3x + 2x = 5x
-1 + 5x + -4x2 = -2x + 4x2 + 2x + -4x2

Reorder the terms:
-1 + 5x + -4x2 = -2x + 2x + 4x2 + -4x2

Combine like terms: -2x + 2x = 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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