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

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


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

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

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

Multiply (-1 + 3x) * (-1 + 3x)
(-1(-1 + 3x) + 3x * (-1 + 3x)) + -1x * x = 0
((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) + -1x * x = 0
((1 + -3x) + 3x * (-1 + 3x)) + -1x * x = 0
(1 + -3x + (-1 * 3x + 3x * 3x)) + -1x * x = 0
(1 + -3x + (-3x + 9x2)) + -1x * x = 0

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

Multiply x * x
1 + -6x + 9x2 + -1x2 = 0

Combine like terms: 9x2 + -1x2 = 8x2
1 + -6x + 8x2 = 0

Solving
1 + -6x + 8x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -4x)(1 + -2x) = 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 + -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 = {0.25, 0.5}

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