(x-1)(3x-1)+x(3x-1)=0

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Solution for (x-1)(3x-1)+x(3x-1)=0 equation: 


Simplifying
(x + -1)(3x + -1) + x(3x + -1) = 0

Reorder the terms:
(-1 + x)(3x + -1) + x(3x + -1) = 0

Reorder the terms:
(-1 + x)(-1 + 3x) + x(3x + -1) = 0

Multiply (-1 + x) * (-1 + 3x)
(-1(-1 + 3x) + x(-1 + 3x)) + x(3x + -1) = 0
((-1 * -1 + 3x * -1) + x(-1 + 3x)) + x(3x + -1) = 0
((1 + -3x) + x(-1 + 3x)) + x(3x + -1) = 0
(1 + -3x + (-1 * x + 3x * x)) + x(3x + -1) = 0
(1 + -3x + (-1x + 3x2)) + x(3x + -1) = 0

Combine like terms: -3x + -1x = -4x
(1 + -4x + 3x2) + x(3x + -1) = 0

Reorder the terms:
1 + -4x + 3x2 + x(-1 + 3x) = 0
1 + -4x + 3x2 + (-1 * x + 3x * x) = 0
1 + -4x + 3x2 + (-1x + 3x2) = 0

Reorder the terms:
1 + -4x + -1x + 3x2 + 3x2 = 0

Combine like terms: -4x + -1x = -5x
1 + -5x + 3x2 + 3x2 = 0

Combine like terms: 3x2 + 3x2 = 6x2
1 + -5x + 6x2 = 0

Solving
1 + -5x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -3x)(1 + -2x) = 0


Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0.3333333333, 0.5}

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