6x(x-1)=(2x+1)(x-1)

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Solution for 6x(x-1)=(2x+1)(x-1) equation: 


Simplifying
6x(x + -1) = (2x + 1)(x + -1)

Reorder the terms:
6x(-1 + x) = (2x + 1)(x + -1)
(-1 * 6x + x * 6x) = (2x + 1)(x + -1)
(-6x + 6x2) = (2x + 1)(x + -1)

Reorder the terms:
-6x + 6x2 = (1 + 2x)(x + -1)

Reorder the terms:
-6x + 6x2 = (1 + 2x)(-1 + x)

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

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

Solving
-6x + 6x2 = -1 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
1 + -6x + x + 6x2 + -2x2 = -1 + -1x + 2x2 + 1 + x + -2x2

Combine like terms: -6x + x = -5x
1 + -5x + 6x2 + -2x2 = -1 + -1x + 2x2 + 1 + x + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
1 + -5x + 4x2 = -1 + -1x + 2x2 + 1 + x + -2x2

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

Combine like terms: -1 + 1 = 0
1 + -5x + 4x2 = 0 + -1x + x + 2x2 + -2x2
1 + -5x + 4x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
1 + -5x + 4x2 = 0 + 2x2 + -2x2
1 + -5x + 4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1 + -5x + 4x2 = 0

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


Subproblem 1
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

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 = {0.25, 1}

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