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

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


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

Reorder the terms:
4x(-1 + 2x) + (2x + -1)(2x + -1) = 0
(-1 * 4x + 2x * 4x) + (2x + -1)(2x + -1) = 0
(-4x + 8x2) + (2x + -1)(2x + -1) = 0

Reorder the terms:
-4x + 8x2 + (-1 + 2x)(2x + -1) = 0

Reorder the terms:
-4x + 8x2 + (-1 + 2x)(-1 + 2x) = 0

Multiply (-1 + 2x) * (-1 + 2x)
-4x + 8x2 + (-1(-1 + 2x) + 2x * (-1 + 2x)) = 0
-4x + 8x2 + ((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) = 0
-4x + 8x2 + ((1 + -2x) + 2x * (-1 + 2x)) = 0
-4x + 8x2 + (1 + -2x + (-1 * 2x + 2x * 2x)) = 0
-4x + 8x2 + (1 + -2x + (-2x + 4x2)) = 0

Combine like terms: -2x + -2x = -4x
-4x + 8x2 + (1 + -4x + 4x2) = 0

Reorder the terms:
1 + -4x + -4x + 8x2 + 4x2 = 0

Combine like terms: -4x + -4x = -8x
1 + -8x + 8x2 + 4x2 = 0

Combine like terms: 8x2 + 4x2 = 12x2
1 + -8x + 12x2 = 0

Solving
1 + -8x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -6x)(1 + -2x) = 0


Subproblem 1
Set the factor '(1 + -6x)' equal to zero and attempt to solve:

Simplifying
1 + -6x = 0

Solving
1 + -6x = 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 + -6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6x = 0 + -1
-6x = 0 + -1

Combine like terms: 0 + -1 = -1
-6x = -1

Divide each side by '-6'.
x = 0.1666666667

Simplifying
x = 0.1666666667

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 = {0.1666666667, 0.5}

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