(2x-1)(3x-1)+(3x-1)(4x-1)-(3x-1)(3x-1)=0

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Solution for (2x-1)(3x-1)+(3x-1)(4x-1)-(3x-1)(3x-1)=0 equation: 


Simplifying
(2x + -1)(3x + -1) + (3x + -1)(4x + -1) + -1(3x + -1)(3x + -1) = 0

Reorder the terms:
(-1 + 2x)(3x + -1) + (3x + -1)(4x + -1) + -1(3x + -1)(3x + -1) = 0

Reorder the terms:
(-1 + 2x)(-1 + 3x) + (3x + -1)(4x + -1) + -1(3x + -1)(3x + -1) = 0

Multiply (-1 + 2x) * (-1 + 3x)
(-1(-1 + 3x) + 2x * (-1 + 3x)) + (3x + -1)(4x + -1) + -1(3x + -1)(3x + -1) = 0
((-1 * -1 + 3x * -1) + 2x * (-1 + 3x)) + (3x + -1)(4x + -1) + -1(3x + -1)(3x + -1) = 0
((1 + -3x) + 2x * (-1 + 3x)) + (3x + -1)(4x + -1) + -1(3x + -1)(3x + -1) = 0
(1 + -3x + (-1 * 2x + 3x * 2x)) + (3x + -1)(4x + -1) + -1(3x + -1)(3x + -1) = 0
(1 + -3x + (-2x + 6x2)) + (3x + -1)(4x + -1) + -1(3x + -1)(3x + -1) = 0

Combine like terms: -3x + -2x = -5x
(1 + -5x + 6x2) + (3x + -1)(4x + -1) + -1(3x + -1)(3x + -1) = 0

Reorder the terms:
1 + -5x + 6x2 + (-1 + 3x)(4x + -1) + -1(3x + -1)(3x + -1) = 0

Reorder the terms:
1 + -5x + 6x2 + (-1 + 3x)(-1 + 4x) + -1(3x + -1)(3x + -1) = 0

Multiply (-1 + 3x) * (-1 + 4x)
1 + -5x + 6x2 + (-1(-1 + 4x) + 3x * (-1 + 4x)) + -1(3x + -1)(3x + -1) = 0
1 + -5x + 6x2 + ((-1 * -1 + 4x * -1) + 3x * (-1 + 4x)) + -1(3x + -1)(3x + -1) = 0
1 + -5x + 6x2 + ((1 + -4x) + 3x * (-1 + 4x)) + -1(3x + -1)(3x + -1) = 0
1 + -5x + 6x2 + (1 + -4x + (-1 * 3x + 4x * 3x)) + -1(3x + -1)(3x + -1) = 0
1 + -5x + 6x2 + (1 + -4x + (-3x + 12x2)) + -1(3x + -1)(3x + -1) = 0

Combine like terms: -4x + -3x = -7x
1 + -5x + 6x2 + (1 + -7x + 12x2) + -1(3x + -1)(3x + -1) = 0

Reorder the terms:
1 + -5x + 6x2 + 1 + -7x + 12x2 + -1(-1 + 3x)(3x + -1) = 0

Reorder the terms:
1 + -5x + 6x2 + 1 + -7x + 12x2 + -1(-1 + 3x)(-1 + 3x) = 0

Multiply (-1 + 3x) * (-1 + 3x)
1 + -5x + 6x2 + 1 + -7x + 12x2 + -1(-1(-1 + 3x) + 3x * (-1 + 3x)) = 0
1 + -5x + 6x2 + 1 + -7x + 12x2 + -1((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) = 0
1 + -5x + 6x2 + 1 + -7x + 12x2 + -1((1 + -3x) + 3x * (-1 + 3x)) = 0
1 + -5x + 6x2 + 1 + -7x + 12x2 + -1(1 + -3x + (-1 * 3x + 3x * 3x)) = 0
1 + -5x + 6x2 + 1 + -7x + 12x2 + -1(1 + -3x + (-3x + 9x2)) = 0

Combine like terms: -3x + -3x = -6x
1 + -5x + 6x2 + 1 + -7x + 12x2 + -1(1 + -6x + 9x2) = 0
1 + -5x + 6x2 + 1 + -7x + 12x2 + (1 * -1 + -6x * -1 + 9x2 * -1) = 0
1 + -5x + 6x2 + 1 + -7x + 12x2 + (-1 + 6x + -9x2) = 0

Reorder the terms:
1 + 1 + -1 + -5x + -7x + 6x + 6x2 + 12x2 + -9x2 = 0

Combine like terms: 1 + 1 = 2
2 + -1 + -5x + -7x + 6x + 6x2 + 12x2 + -9x2 = 0

Combine like terms: 2 + -1 = 1
1 + -5x + -7x + 6x + 6x2 + 12x2 + -9x2 = 0

Combine like terms: -5x + -7x = -12x
1 + -12x + 6x + 6x2 + 12x2 + -9x2 = 0

Combine like terms: -12x + 6x = -6x
1 + -6x + 6x2 + 12x2 + -9x2 = 0

Combine like terms: 6x2 + 12x2 = 18x2
1 + -6x + 18x2 + -9x2 = 0

Combine like terms: 18x2 + -9x2 = 9x2
1 + -6x + 9x2 = 0

Solving
1 + -6x + 9x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -3x)(1 + -3x) = 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 + -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
Solution
x = {0.3333333333, 0.3333333333}

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